>"perfect arguments don't exi-"
"perfect arguments don't exi-"
Joshua Green
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Henry Russell
Math doesn't need to talk about real-life objects, just like a novel doesn't need to talk about real-life events. You can create theorems about irrational numbers and infinite sequences, just like you can write a novel about dragons and wizards.
John Gomez
back to your fantasy land, physicists. You can't fool me with your hand-wavy drivel
Brody Morales
real number might be real but most of them are irrational!! haha
*zeno's laterally away*
Owen Sanders
>laterally
pretty sure you're not allowed to do that
Nicholas Ward
I was wondering just the other day what Veeky Forums thought of Wildberger.
One of the big thing that I think he's missing is that all math is ultimately based on murky intuitions *anyway*. His complaint is that we don't know exactly what an "infinite set" or a "real number" is, but guess what, we don't exactly know what a "natural number" is, either. You can appeal to a vague gut feeling of somehow being able to "conceive" of the number 5 as an abstract object, but I'll just tell you that I have the same kind of feelings about infinite sets. Most people are happy to take infinite sets as basic undefined objects. He isn't. The rest of us aren't "wrong".
What I've also always found odd is that he's happy to deal with infinity in some contexts but not others.
For instance, he complains that we can never prove that e + pi = pi + e, since both numbers are irrational, so we can't just compute the number on each side of the identity ("roll up our sleeves", as he says) and compare them to each other to check. Whereas if I claim a + b = b + a for all rationals, I can check that on any particular pair of rationals a, b.
But when I say e + pi = pi + e, it's a shorthand for a complicated statement involving nested intervals, or Dedekind cuts, or whatever. By the symbols "e", "pi", "e+pi" or "pi+e", I mean a certain algorithm for calculating a list of decimal digits, and by the equal sign, I mean those algorithms output the same sequence no matter how far you carry it. I don't see how "no matter how far you go, all the decimal digits will be equal" is any more objectionable than "no matter how many you try, all rational numbers will verify a + b = b + a", or "no matter how far you go, you can find another prime number".
Cooper Watson
>Dedekind cuts
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Easton Price
Xavier Taylor
tfw its illegal to go sideways :^(
Grayson Peterson
So because Mr Wildberger does not believe in sets, the reals do not exist?