How many perfect are there compared to natural numbers

>>9019375
>But how can there be more squares than natural numbers if for every natural number there exists one square?
there aren't more squares, for the reason you just said

n <-> n^2 is a bijection so they have the same cardinality

>>9019375
That capsule also ripped off a dudes legs

>>9019378

What if you started counting and then kept track of how many squares and non-squares you found

Could not it be proven that after a certain point the amount of non-squares will always exceed the amount of squares?

>>9019387
if you're just keeping a running tally then of course after any finite amount of time you'll have counted more non-squares than squares, unless you stop counting after 1

File: rufkm.jpg (5KB, 227x222px) Image search: [Google]

5KB, 227x222px

>have two infinite sets
>say one has "more" than the other

>>9019389
or stop counting after 4 i guess

if you count n numbers there's at most sqrt(n) squares, and n-sqrt(n) non-squares, for n>2 n-sqrt(n) > sqrt(n) so there's more non-squares

>>9019396

but every single non-square has exactly 1 square associated with it

>>9019398
>but every single non-square has exactly 1 square associated with it
yes, see
>>9019378
>n <-> n^2 is a bijection so they have the same cardinality

>>9019390
Oh look, I found a fucking dipshit.

>>9019384
Source?

there exists a bijection between [math]\mathbb{N}[/math] and [math]\{ n^2 \mid n \in \mathbb{N}\}[/math], given by [math]n \mapsto n^2[/math]
in layman's terms, there are precisely as many natural numbers as there are squares (at least from the point of view of modern mathematics)
/thread

>>9019402
>Oh look, I found a fucking dipshit.
Yeah, me too.

>>9019390
There are more real numbers than natural numbers.

>>9021037
That's not a bijection (no natural number maps to 2, for example).

>>9021042
>That's not a bijection (no natural number maps to 2, for example).
2 isn't in the codomain, so that's not an argument for non-bijectivity

>>9019375
what if something goes wrong? does that capsule have an ejector seat?

>>9021054
yes of course it does. and if the ejector seat fails you can just eject your fucking brain out of your skull with a pistol you stupid piece of shit.

>>9021042
>That's not a bijection (no natural number maps to 2, for example).
it is, look at the codomain

>>9021062
but would my brain deploy a parachute?

File: escape capsule b58.jpg (84KB, 720x384px) Image search: [Google]

84KB, 720x384px

>>9019384
Lol I can see how that might happen.

>index two sets over N
>add the strain of an elementary operation
>be amazed that there is a bijection between the two

>>9021147
2 is not in the codomain

>>9019389
You are enforcing an order by counting sequentially.

Say you counted one integer and two squares repeatedly, i.e.
1, 1,4, 2, 9,16, 3...
If you counted infinitely, by your logic there are twice as many squares. This is why this is not a proper way of addressing the problem, as it leads to contradictions

>>9021149

so are you talking about numbers or something?