Proof 0=1 • page 7/7 • Off-Topic Discussion • lichess.org

I tried to edit my comment, but it's failing so here's a new one

1a: (Doesn't change anything)
I was thinking about Aleph(0), aka Countable Infinity, the smallest infinity, but I guess this applies to other infinities.

1b:
Generally people prove infinities are the same/different by
taking two sets (collections) of things.

Like { apple, orange } vs { 1, 2 }
There is a 1:1 correspondence with both of these sets, (apple maps to 1 & orange maps to 2), so they're the same size.
And if the sets are the same size, the infinities are the same.

{ 0, 1, 2, 3, ... } is the same size as { 0, 2, 4, 6, ... }
0 maps to 0
1 maps to 2
n maps to 2n

So... every number "fits".

1c.
Well, the difference between the two lines might seem bigger and bigger....
But the second line will eventually extend to infinity.
And the first line also extends to infinity.

So visually, they're... the same?
(Bad argument)

I tried to edit my comment, but it's failing so here's a new one 1a: (Doesn't change anything) I was thinking about Aleph(0), aka Countable Infinity, the smallest infinity, but I guess this applies to other infinities. 1b: Generally people prove infinities are the same/different by taking two sets (collections) of things. Like { apple, orange } vs { 1, 2 } There is a 1:1 correspondence with both of these sets, (apple maps to 1 & orange maps to 2), so they're the same size. And if the sets are the same size, the infinities are the same. { 0, 1, 2, 3, ... } is the same size as { 0, 2, 4, 6, ... } 0 maps to 0 1 maps to 2 n maps to 2n So... every number "fits". 1c. Well, the difference between the two lines might seem bigger and bigger.... But the second line will eventually extend to infinity. And the first line also extends to infinity. So visually, they're... the same? (Bad argument)