>Infinite sets thread
Convince me to escape from the prison of finitism and ultrafinist mathematics. Burger has some compelling arguments for finitism and the nonexistence of infinite sets.
>>8037207
>some compelling arguments
>Have you ever seen an infinity before?
>No, you haven't
>Does it make sense for this drumstick to be infinitely long?
>No, it doesn't
>Therefore infinite sets don't exist, QED.
It certainly convinced me.
>>8037244
Why shouldn't we try to re-construct analysis without relying on infinite sets?
>>8037207
Infinity is inherently flawed. It leads to paradoxes such as 0.999... = 1
>>8037264
B-but 0.999... does equal 1!
>captcha: 111
>>8037287
An infinite number cannot equal a finite number.
>>8037249
Because analysis isn't real life. Do you reject basic geometry because you can't draw a perfect circle?
>>8037292
0.999... = string of infinite nines. If it were not infinite, then it would not equal one.
>>8037294
>you can't draw a perfect circle?
false
>>8037294
so you're saying we shouldn't even try because you think its impossible?
>religion is that way
>>8037345
I'm saying there's no reason to try. What benefit is there to doing math with only finite sets? We have no problems, fundamental or otherwise, coming from using infinite sets, and the math we have is incredibly successful at describing reality. Can you give a valid for redoing all of mathematics so restrictively?
>>8037351
because if mathematics is successful then we can end this fucking debate of whether or not analysis is "logically rigorous"
If we add 1 to a natural number then we will get natural number. Let N be set of all naturals, then it has greatest element n, so that for every m in N n>=m. We know that n+1>n is natural, this leads to contradiction, so N is infinite so infinite sets exist
>>8037365
I think most math is based on the assumption of an infinite set, not the exhibition of one.
>>8037300
Dude you can't, in the same way you cannot have 100 percent purity in a chemistry.
Look here for example:
>http://io9.gizmodo.com/5982714/the-most-perfect-sphere-ever-made-tests-einsteins-theories
(right now I can't find a better link, though)
>>8037394
>io9
pure cancer
>>8037356
There is no debate though. Wildburger has no arguments and fundamentally misunderstands what axioms are.
>>8037419
finitism is a serious and populated branch of mathematics
certainly it's not the mainstream opinion, but it's not exactly a fringe domain solely for nutjobs
>>8037287
That's actually true, it does equal 1!
>>8037419
He understands perfectly well what axioms are. He just prefers to do math without modern axiomatic systems.
>>8037446
>finitism is a serious and populated branch of mathematics
nah
>>8037365
>Let N be set of all naturals
wew lad
>>8037365
Dumbass. The construction of the natural numbers relies on the axiom of infinity. You haven't shown that your largest number [math]N[/math] has [math]N +1[/math] in [math]\mathbb{N}[/math], instead you just say "hurr durr we know that it is" like a fucking retard.
>>8038117
Ya he basically just said
>assume N is infinite
>rambles cretinous regurgitation
>therefore N is infinite
>>8037294
No, we reject pi because we cannot draw a perfect circle.
