Axiom 3: The Most Important Axiom in Math

[@danii7120]

Fantastic video! I've been self studying set theory and was having trouble understanding the notation for this axiom, but this video cleared it up fantastically. Thank you!

[@maryj7423]

I recently rediscovered math (or rather discovered it for the first time) and I loved this video, especially the clip at the end, (I didn't see coming!) he was so articulate and wise. Thank you.

[@dukewilliam1st]

the last bit proves that mathematicians can be good philosophers

[@eduardosuela7291]

Actually, maths and philosophy need similar mindsets in reasoning. Russell himself summarised his life (i don't have the exact words), quote: When i was young and strong, i was a mathematician. When i still had some energy, i became a philosopher. Finally, when i was utterly useless old man, my only job was to be a politician. Even as a politician, he indeed did great things. Some of those being "Atoms for peace" manifesto with Einstein and defended liberty and science from negationists and religious fanatics.

[@alejrandom6592]

There is a mathematician within every philosopher and there is a philosopher within every mathematician. At the bottom of math you find the base of philosophy, and at the bottom of philosophy you find the base of math. Both ask the same question: What is true?

[@spiderjerusalem4009]

Mathematics is applied philosophy

[@jeronimomendez1007]

Amazing video! I am in my second year in my math major and set theory is one of my favourite subjects. This video made the third axiom my favourite one.

[@guzmat]

Glad it helped! I'm preparing the next videos: axioms 4,5 and 6 will be together ... then the definition of numbers and N ... then axiom 7 and Infinity.

[@jeronimomendez1007]

@@guzmat Amazing! I can't wait

[@alejrandom6592]

I always heard you can prove anything from a contradictory statement, but never seen the actual construction. Nice

[@gloriakalengelayi8294]

Hi, I’m not very good at understanding the mathematical explanation of the axioms or paradox’s. But I understand the simple explanations. For example I’m watching your axiom playlist. So I watched the video of you doing the catalog. If I had just watched the mathematical explanation using the Set I would be confused. But since I watched the video before and understood that very well, the math explanation wasn’t so confusing. Please do continue to use the basic explanation with no maths along side the mathematical explanation of the same thing. It really helps thanks.

[@guzmat]

Thank you!!! I really appreciate your comment, it really helps me to understand what is better. Ciao!!!

[@robertveith6383]

* paradoxes

[@yukuseru2195]

May I ask the reference of the outro video you have given? 7:03

[@GuzMat-matematicas]

I'm travelling ... i Will answef you when i go back home ...

[@guzmat]

check the description of this video: kzbin.info/www/bejne/n5nEc2t3e7SbkNE

[@dadsonworldwide3238]

How successful social behavior like curses and blessings becomes addition and subtraction into marketplace is amazing and telling in ways I can't believe it took so long to learn ourselves and how we Triangulate readability and judge thermodynamical systems with legibility. A truly amazing interactive measure. The keys to the cosmos textualism methodology objectivism truly separated us from ancient world bumbling around with shared knowledge just no way to doing anything with it.

[@jonathanlivengood767]

Maybe worth noting that there are non-classical, paraconsistent logics within which derivations of the sort you sketched (say, of 1=2 from an arbitrary contradiction) don't work. For example, in typical relevant logics, disjunctive syllogism is not valid.

[@guzmat]

Yes, thanks for mentioning that ... I was wondering about the possibility of explaining a bit of that but in the end I thought it was too much ... thank you , ciao!!!

[@michaelsharpe4217]

The barber shaves all men who do not shave himself. Who shaves the Barber?

[@dominiqueubersfeld2282]

For Terrence Howard, the most important axiome is 1x1=2

[@pocojoyo]

wouldnt you say the "Axiom" of Choice is more important than the Axiom of Specification ?

[@guzmat]

that's interesting ... we'll discuss that in a few videos from now ...

[@attica7980]

Actually, the real power of Zermelo-Fraenkel set theory comes from the axiom scheme of replacement, invented by Abraham Fraenkel. Replacement implies specification, so the axiom of specification can be removed. Replacement asserts that the image of a set under a function (described by a logic formula) is also a set. For each logic formula in the language of set theory there is an axiom, so replacement consists of infinitely many axioms, called an axiom scheme.

[@TryN0]

U Look Like Clever 😜😺

[@HugoHabicht12]

Well, if you don’t like it, you just define a solution out of the blue. Haha, that’s maths.

[@guzmat]

Exactly! :D

[@victorhiggins2118]

Women do shave