Prove that sqrt(2) exists [ILIEKMATHPHYSICS]

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This video is part of the “Real Analysis” section of the “All About Proofs in Mathematics” series I am making.

Thanks and enjoy the video!

All About Proofs in Mathematics playlist:
  1. ILIEKMATHPHYSICS
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Комментарии
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Great video man. Thanks for being that organized, it has been really helpful for me :)

vasylhryhoriev
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Love the fact you speed up when writing, amazing quality of life edit. Keep up the good work, love watching all your videos!

craftinators
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Fantastic video as always! I’m guessing you’re a Pure Math major as well?

TheRiverNyle
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Great video, thank you! The clarity of your explanations in your videos is outstanding!

I have one question: Couldn't it be, that the assumption r^2=2 also leads to a contradiction? This is possible with statements which are self-contradictory, for example in the case of Russells Paradox. How can we know for sure, that in this case we have no self-contradiction? I also have this question in general, so how we can know this in any specific case. (Sorry for my english, it's not my first language :D)

Greetings!

vincentv.
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mathematicians love this kind of proof where you define a set and then say "oh look, by the axioms of set theory this thing exists or it's this or that way". I'm not more impressed than a proof based on an algorithm or a Calculus-based proof for the intermediate value or something of that sort. It's just playing pretend that Set Theory is somehow more "fundamental". /end of my rant / sorry for the rant

radadadadee