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 International Skeptics Forum Continuation Deeper than primes - Continuation 1/3*9

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 2nd July 2020, 06:38 AM #41 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,259 Originally Posted by jsfisher ... and <= is the relationship that is the subject of the definition. jsfisher, is it possible to define Cardinality only by <= relationship from set A to set B (written as A <= B)? If no, then cardinality is a part of the definition of Cardinality as shown, for example, in http://www.internationalskeptics.com...4&postcount=40 . If you disagree with me, then please air your view about this post. Thank you. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 2nd July 2020 at 06:41 AM.
 2nd July 2020, 06:44 AM #42 zooterkin Nitpicking dilettanteAdministrator     Join Date: Mar 2007 Location: Berkshire, mostly Posts: 46,807 Originally Posted by doronshadmi jsfisher, is it possible to define Cardinality only by <= relationship from set A to set B (written as A <= B)? If no, then cardinality is a part of the definition of Cardinality as shown, for example, in http://www.internationalskeptics.com...4&postcount=40 . If you disagree with me, then please air your view about this post. Thank you. Doron, jsfisher is not defining ‘cardinality’, he is defining ‘relative cardinality’, the relationship between the cardinalities of two sets. __________________ The whole problem with the world is that fools and fanatics are always so certain of themselves, and wiser people so full of doubts.Bertrand Russell Zooterkin is correct Darat Nerd! Hokulele Join the JREF Folders ! Team 13232 Ezekiel 23:20
 2nd July 2020, 06:56 PM #43 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,942 Originally Posted by doronshadmi jsfisher, is it possible to define Cardinality only by <= relationship from set A to set B (written as A <= B)? As zooterkin properly points out, I did not define cardinality. I defined a relationship. I chose "<=" as the symbol for this dyadic boolean relationship. Cardinality of a set is normally indicated by vertical bars to either side of the set name -- a convention so well known to almost everyone that explicit mention of the convention should not be required. In context, A and B would be interpreted as symbols for arbitrary sets -- another convention for which no explicit mention should be necessary. To define the relationship, it must be presented with operands so the operands can participate in the definition. Ergo, "|A| <= |B|" is the thing being defined. I.e., "the relationship symbolized by <= with operands, |A| and |B|". And "there exists an injection from A to B" is the definition. So, once again, cardinality is not being defined, but a relationship between the cardinality of two sets is being defined. This is not third grade math, so please stop trying to apply third grade concepts to it. __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 3rd July 2020, 06:06 AM #44 Little 10 Toes Master Poster     Join Date: Nov 2006 Posts: 2,235 Thank you to zooterkin and jsfisher. I knew what I was trying to say, I just wasn't the right terms. __________________ I'm an "intellectual giant, with access to wilkipedia [sic]" "I believe in some ways; communicating with afterlife is easier than communicating with me." -Tim4848 who said he would no longer post here, twice in fact, but he did.
 4th July 2020, 07:18 AM #45 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,259 Originally Posted by zooterkin Doron, jsfisher is not defining ‘cardinality’, he is defining ‘relative cardinality’, the relationship between the cardinalities of two sets. Please look at http://www.internationalskeptics.com...postcount=3448 do you see there that jsfisher literally stats that he defines ‘relative cardinality’? __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video.
 4th July 2020, 07:26 AM #46 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,942 Originally Posted by doronshadmi Please look at http://www.internationalskeptics.com...postcount=3448 do you see there that jsfisher literally stats that he defines ‘relative cardinality’? This is not the Politics Section. Is there a point you care to make that doesn't require hyper-parsing, spin-doctoring, misreading, and misrepresenting what's posted? __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 4th July 2020, 08:26 AM #47 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,259 Originally Posted by jsfisher As zooterkin properly points out, I did not define cardinality. I defined a relationship. Sorry jsfisher, here is what you have said: Originally Posted by jsfisher For that matter, you need to be clear what you mean by "cardinality". No, wait, better still, I will provide you a definition of cardinality for the purposes of this discussion. Cardinality is a relative measure of "size" of sets where |A| <= |B| if and only if there exists an injection from A to B. (The meanings for strict equality and strict inequality of cardinalities follow directly.) Note that this definition requires only the introduction of mappings into the set theory. No mention of a definition of Relative cardinality, isn't it? So, after some number of posts and a little help from zooterkin, your definition of Cardinality, is not a definition of Cardinality, but it is actually a definition of a relative measure between the cardinalities of two arbitrary sets. In other words, your determination of the need to be clear is not fulfilled. --------------------- Any way, 'The definition of a relative measure between the cardinalities of two arbitrary sets' has a motivation behind it, which is: To be general enough, in order to not distinguish between finite or infinite sets. ZF(C) is actually a theory of sets, where its Axiom Of Infinity, is not actually Axiom Of Infinity unless more things are involved with it. This style of work is done for the name of generalization, such that any given statement does not stand for its own, but depends on the interpretation that is given to it according to the rules of a given context. In other words, traditional mathematics is based on the of Philosophy of relativism (https://plato.stanford.edu/entries/relativism/) and jsfisher actually demonstrates it, no matter what he argues about the independence of traditional mathematics in any philosophical issues. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 4th July 2020 at 08:28 AM.
 4th July 2020, 10:13 AM #48 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,259 Originally Posted by jsfisher This is not the Politics Section. Is there a point you care to make ... ? Yes jsfisher, this section is about Religion and Philosophy, in case that you have missed it. Furthermore, what is called traditional mathematics is deeply rooted in Philosophy, as shown in http://www.internationalskeptics.com...2&postcount=47 . __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video.
 4th July 2020, 10:29 AM #49 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,259 Now back to the current issue, my answer to http://www.internationalskeptics.com...postcount=3487 is given in http://www.internationalskeptics.com...8&postcount=31 . According to a reasonable criticism (that unlike you, is aware of the philosophical point of view of it) it will be changed. If you still reject Philosophy as a source of motivation for mathematical work, any mathematical work, then there is no real discussion between us, because all you care is to show how Philosophy is disconnected from actual mathematical work (which is by itself, no more no less than some philosophical point of view). Your particular philosophical view of mathematics is actually like a string that penetrates trough all your posts since our first dissuasion that was done almost 12 years ago. I have learned a lot from your particular philosophical view of mathematics, and tried to air my particular philosophical view of mathematics, which unlike your philosophical point of view, does not reject philosophy as an actual factor of mathematical work, any mathematical work. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 4th July 2020 at 10:41 AM.
 4th July 2020, 03:24 PM #50 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,942 Originally Posted by doronshadmi If you still reject Philosophy as a source of motivation for mathematical work, any mathematical work, then there is no real discussion between us, because all you care is to show how Philosophy is disconnected from actual mathematical work (which is by itself, no more no less than some philosophical point of view). You are just now figuring out that the whole point of building Mathematics on a axiomatic basis is to be disconnected, as you say, from Philosophy? You need to pay more attention. Philosophy credits itself with having "really good ideas"TM, which it may or may not have, but it does not have the consistency nor any sort of rigor essential for advancing Mathematics. The Dark Ages are over; time you moved on. __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 5th July 2020, 01:15 AM #51 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,259 Originally Posted by jsfisher time you moved on. You can move on as much as you like, Philosophy is an essential factor of any mathematical, as very simply demonstrated in http://www.internationalskeptics.com...2&postcount=47 . __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video.
 5th July 2020, 01:33 AM #52 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,259 Originally Posted by jsfisher ... but it does not have the consistency nor any sort of rigor essential for advancing Mathematics. This is no less no more than your philosophical point of view about the relations between Mathematics and Philosophy. This approach of separated islands of context dependent mathematical frameworks, is a direct result of the understanding that most of these separated and, so called, rigor contexts dependent islands (which are able to deal with Arithmetic) can't prove their own consistency by finitely many axioms (the end of Hilbert's program, as a result of Godel's incompleteness theorems). The end of Hilbert's program, is one of the reasons why mathematicians stopped dealing with "big ideas" (philosophical notions) and reduced their work to "small ideas" (the technical mechanism of rigorous methods). ---------------------- Please critisize http://www.internationalskeptics.com...8&postcount=31 and it's links, by your, so called, rigorous mathematical working methods. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 5th July 2020 at 02:23 AM.
 5th July 2020, 02:17 AM #53 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,259 Originally Posted by jsfisher The Dark Ages ... By the way, I suggest you to learn about what is called "The Dark Ages ..." before you use it in your posts. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video.
 5th July 2020, 02:32 AM #54 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,259 Originally Posted by jsfisher You are just now figuring out that the whole point of building Mathematics on a axiomatic basis is to be disconnected, as you say, from Philosophy? You need to pay more attention. You need to pay more attention of the fact that most of the interesting mathematical frameworks that are based on axioms, can't prove their own consistency, so you are working most of the time in a very shallow water, exactly because of what you call rigor. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 5th July 2020 at 03:29 AM.
 5th July 2020, 07:50 AM #55 Little 10 Toes Master Poster     Join Date: Nov 2006 Posts: 2,235 Please provide evidence of this claim. __________________ I'm an "intellectual giant, with access to wilkipedia [sic]" "I believe in some ways; communicating with afterlife is easier than communicating with me." -Tim4848 who said he would no longer post here, twice in fact, but he did.
 5th July 2020, 09:48 AM #56 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,942 Originally Posted by Little 10 Toes Please provide evidence of this claim. He's right about that consistency thing. Gödel’s second Incompleteness Theorem proved that any consistent formal system in Mathematics rich enough to include arithmetic cannot prove its own consistency. Be that as it may, though, the point is irrelevant in the current discussion arc. Mathematics shuns inconsistency even though it cannot usually guarantee its absence while Philosophy cherishes it. __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 6th July 2020, 04:25 AM #57 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,259 Originally Posted by jsfisher He's right about that consistency thing. Gödel’s second Incompleteness Theorem proved that any consistent formal system in Mathematics rich enough to include arithmetic cannot prove its own consistency. Be that as it may, though, the point is irrelevant in the current discussion arc. Mathematics shuns inconsistency even though it cannot usually guarantee its absence while Philosophy cherishes it. It is relevant, as shown in http://www.internationalskeptics.com...4&postcount=52 , and my argument is not about Mathematics vs. Philosophy, but it is about the philosophical motivations that actually deeply influence on the rigorous mechanism of any mathematical work. As for the current discussion Zermelo and his followers vary carefully established a theory of sets such that it will preserve Cantor's notions of infinite sets in terms of actual infinity. For example, Cardinality is not defined directly by observations of natural numbers (as done for example in http://www.internationalskeptics.com...8&postcount=31, and was improved by jsfisher's criticism) , but it is defined indirectly through a relative measurement (a one-to-one mapping in this case) from the members of one set (called A) to the members of another set (called B), in such a way that enables to plug in Cantor's transfinite system (which is actually the translation of a philosophical notion of infinity in terms of a set that actually has infinitely many members that are taken as a complete whole). By this indirect definition of Cardinality one enables to suddenly jump into a measurement unit like aleph-0, like a third degree magician, which truly believes that that by indirect definition of Cardinality the audience will not pay attention to his inconsistent trick. Unlike jsfisher indirect approach, which also ignore the philosophical motivations behind his indirect definition of cardinality, http://www.internationalskeptics.com...8&postcount=31 does not need any indirect methods in order to define Cardinality, and I do not try to hide my philosophical motivations, which argue that any infinite collection (where an infinite set is a particular case of an infinite collection) is no more than potentially infinite since its accurate size is by definition not satisfied. By going beyond the notion of collections, and by using philosophical direct approach of the discussed subject, actual infinity is essentially non-composed, as already demonstrated in http://www.internationalskeptics.com...postcount=3285 . __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 6th July 2020 at 04:57 AM.
 14th July 2020, 11:22 PM #58 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,259 Originally Posted by jsfisher Philosophy credits itself with having "really good ideas"TM, which it may or may not have, but it does not have the consistency nor any sort of rigor essential for advancing Mathematics. The Dark Ages are over; time you moved on. Let's move on jsfisher. So according to traditional mathematics: 1) Cardinality is a relative measure of "size" of sets where |A| <= |B| if and only if there exists an injection from A to B. 2) The ZF(C) axiom of infinity has two properties: Property 1: ∅ ∈ I Proeprty 2: ∀ x ∈ I ( ( x ∪ { x } ) ∈ I ) Please (by using (1),(2) and (if needed) more ZF(C) axioms) rigorously establish I as an infinite set (which means that its cardinality is strictly greater than any natural number (where 0 is also taken as a natural number)). __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 14th July 2020 at 11:28 PM.
 15th July 2020, 07:52 AM #59 Little 10 Toes Master Poster     Join Date: Nov 2006 Posts: 2,235 Why? If you read the Axion of Infinity, it already postulated that the set I is infinite. __________________ I'm an "intellectual giant, with access to wilkipedia [sic]" "I believe in some ways; communicating with afterlife is easier than communicating with me." -Tim4848 who said he would no longer post here, twice in fact, but he did.
 15th July 2020, 04:53 PM #60 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,942 Originally Posted by Little 10 Toes Why? If you read the Axion of Infinity, it already postulated that the set I is infinite. Actually, it doesn't. The Axiom establishes that there exists a set meeting two properties. You need to define what it means for a set to be infinite before you can establish that that set meets the definition. The normal approach to that is to adopt a measure of set size, and then it follows. __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 15th July 2020, 05:09 PM #61 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,942 Originally Posted by doronshadmi Let's move on jsfisher. So according to traditional mathematics: 1) Cardinality is a relative measure of "size" of sets where |A| <= |B| if and only if there exists an injection from A to B. No, cardinality, as a relative measure of set size, can be defined by defining a relationship between the sizes of two sets. Id est, |A| <= |B| if and only if there exists an injection from A to B. Quote: 2) The ZF(C) axiom of infinity has two properties: Property 1: ∅ ∈ I Proeprty 2: ∀ x ∈ I ( ( x ∪ { x } ) ∈ I ) No, the Axiom establishes the existence of (at least one) set, I, that has those two properties. Quote: Please (by using (1),(2) and (if needed) more ZF(C) axioms) rigorously establish I as an infinite set (which means that its cardinality is strictly greater than any natural number (where 0 is also taken as a natural number)). Why should I do that? You are the one trying to discredit "traditional mathematics." The burden to prove or disprove whatever it is that establishes your claim lies with you. __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 16th July 2020, 04:47 AM #63 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,942 Originally Posted by doronshadmi Jsfisher, please move on by consistently and rigorously establish the highlighted parts, which have been taken from your quote. You are the one with something to prove (or disprove), not me. These attempts of yours to reverse responsibilities or divert to side topics do not advance your cause. It would be especially good for you to start with a statement of just what is it you are claiming -- a nice, simple declaration of your treatise. Is that too much to ask? __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 17th July 2020, 06:01 AM #65 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,942 Originally Posted by doronshadmi In order to actually do that, please consistency and rigorously support your own highlighted parts (seen in http://www.internationalskeptics.com...2&postcount=62). It would be especially good for you to start with a statement of just what is it you are claiming -- a nice, simple declaration of your treatise. Is that too much to ask? __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 17th July 2020, 08:24 AM #66 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,259 Originally Posted by jsfisher It would be especially good for you to start with a statement of just what is it you are claiming -- a nice, simple declaration of your treatise. Is that too much to ask? It would be especially good for you to consistency and rigorously (which is, as you say, "essential for advancing Mathematics") establish the highlighted parts, which have been taken from your quote (seen in http://www.internationalskeptics.com...2&postcount=62). Is that too much to ask? __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 17th July 2020 at 08:33 AM.
 17th July 2020, 09:42 AM #67 Little 10 Toes Master Poster     Join Date: Nov 2006 Posts: 2,235 Originally Posted by jsfisher It would be especially good for you to start with a statement of just what is it you are claiming -- a nice, simple declaration of your treatise. Is that too much to ask? It appears the answer is yes. __________________ I'm an "intellectual giant, with access to wilkipedia [sic]" "I believe in some ways; communicating with afterlife is easier than communicating with me." -Tim4848 who said he would no longer post here, twice in fact, but he did.
 18th July 2020, 08:10 AM #71 Little 10 Toes Master Poster     Join Date: Nov 2006 Posts: 2,235 Just to be clear doronshadmi, your issue is about how mathematics defines cardinality? Nothing else, just how cardinality is defined? A simple Yes/No answer is fine. Edit: Once your viewpoint is clear, it can be addressed. __________________ I'm an "intellectual giant, with access to wilkipedia [sic]" "I believe in some ways; communicating with afterlife is easier than communicating with me." -Tim4848 who said he would no longer post here, twice in fact, but he did. Last edited by Little 10 Toes; 18th July 2020 at 08:23 AM.
18th July 2020, 11:36 PM   #73
Penultimate Amazing

Join Date: Mar 2008
Posts: 13,259
Originally Posted by jsfisher
It appears you are suggesting that there is something wrong with Mathematics for having ways to measure the size of a set. Is that right?
I claim that the measure of the size of a non-finite set, is not done consistently and rigorously (which means that it is done arbitrarily) by traditional mathematics.

Originally Posted by jsfisher
You would prefer cardinality not be defined?
In http://www.internationalskeptics.com...1&postcount=43 you explicitly state that
Originally Posted by jsfisher
So, once again, cardinality is not being defined, but a relationship between the cardinality of two sets is being defined.
So, cardinality is not being defined by traditional mathematics.

In that case, why do you asking me if I "would prefer cardinality not be defined?" when you are explicitly state that (by traditional mathematics) "cardinality is not being defined"?
Originally Posted by jsfisher

-------------------------------------------------------------------

As for me, I prefer cardinality to be defined without eliminating the difference between finite and non-finite cardinality, for example:

1) I do not need iff in order to define Cardinality by the members of the set of natural numbers (notated as N), where natural numbers (including number 0) are naturally understood (no extra maneuvers are needed).

2) I provide symbols to the concepts "less than", "equal to", "greater than" (which I tend to replace by "more than") which are naturally understood (no extra maneuvers are needed).

3) I use iff in a vary simple way in case of relative measure, between two arbitrary sets A and B, where their cardinalities (what is compared) and the terms of how they are compared are simply and intuitively addressed, because of the simple use of iff.

4) By being simple and intuitive in definitions 1 and 2, I am able to very simply define finite (definition 3) and non-finite (definition 4) sets, without any need to add anything, which are not already given by definitions 1 to 4.

5) Definition 5 very simply addresses non-strict inequality as a range between strict inequality (< or >) and equality (=).

Once again you are invited to criticize what is written in this post and in http://www.internationalskeptics.com...9&postcount=15 post.

Thank you.

 Edited to fix quote link. Please be careful when editing tags. Posted By:zooterkin
__________________
That is also over the matrix, is aware of the matrix.

That is under the matrix, is unaware of the matrix.

For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video.

Last edited by zooterkin; 19th July 2020 at 05:42 AM.

 18th July 2020, 11:47 PM #74 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,259 Originally Posted by Little 10 Toes Just to be clear doronshadmi, your issue is about how mathematics defines cardinality? Nothing else, just how cardinality is defined? A simple Yes/No answer is fine. Edit: Once your viewpoint is clear, it can be addressed. Little 10 Toes, in case that you have missed it, Cardinality is not defined by traditional mathematics. I claim that it must be defined. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video.
 19th July 2020, 07:09 AM #75 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,942 Originally Posted by doronshadmi I claim that the measure of the size of a non-finite set, is not done consistently and rigorously (which means that it is done arbitrarily) by traditional mathematics. What an odd thing to say. For one, arbitrariness has nothing to do with rigor and consistency. For another, where is the inconsistency in defining a relationship by "|A| <= |B| if and only if there is an injection from A to B"? Where is the lack of rigor? __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 19th July 2020, 07:21 AM #76 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,942 Originally Posted by doronshadmi In http://www.internationalskeptics.com...1&postcount=43 you explicitly state that So, cardinality is not being defined by traditional mathematics. Subtlety and nuance escape you. I did not define cardinality, at least not directly. Euclidean Geometry does not define point (directly), nor does ZF Set Theory define set (directly). Instead, ZF Set Theory provides a set of axioms and axiom schema that characterize set properties; Euclidean Geometry characterizes points by way of its postulates; and I defined a relationship sufficient for comparing cardinalities of sets. Guess what that does. __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 20th July 2020, 03:46 AM #77 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 13,259 Originally Posted by jsfisher Instead, ZF Set Theory provides a set of axioms and axiom schema that characterize set properties; ... ; and I defined a relationship sufficient for comparing cardinalities of sets. Guess what that does. Once again you are not consistently and rigorously demonstrate how ZF and your "relationship sufficient for comparing cardinalities of sets" establish a set with non-finite cardinality. Your evasion has be noted. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 20th July 2020 at 03:47 AM.
 20th July 2020, 04:07 AM #78 jsfisher ETcorngods survivorModerator     Join Date: Dec 2005 Posts: 22,942 Originally Posted by doronshadmi Once again you are not consistently and rigorously demonstrate how ZF and your "relationship sufficient for comparing cardinalities of sets" establish a set with non-finite cardinality. Your evasion has be noted. If there is a point you would like to make, do so. I have no interest in being your teacher at this point. And that is not at all being evasive. I am just not falling for your reversal of responsibilities. __________________ A proud member of the Simpson 15+7, named in the suit, Simpson v. Zwinge, et al., and founder of the ET Corn Gods Survivors Group. "He's the greatest mod that never was!" -- Monketey Ghost
 20th July 2020, 05:05 AM #80 Belz... Fiend God     Join Date: Oct 2005 Location: In a post-fact world Posts: 91,292 Twelve years and still going... __________________ Master of the Shining Darkness "My views are nonsense. So what?" - BobTheCoward

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