yuuki ゆうき(金野裕希)@yuukikonno@mastodon.social

actually, there's infinitely many infinite numbers.

actually, the number of natural, integer, and rational numbers are all the same.

that infinite number is called ℵ₀ (aleph zero) or ℶ₀ (beth zero).

Cantor (1874) proved that the number of reals is larger than that.¹
that is called 𝔠 = 2^ℵ₀ = ℶ₁ (beth one).

the idea that having the same number is the same as having a 1-1 correspondence is called
• Hume's principle.¹

¹ neither Hume nor Galileo thought it applied to , tho (unlike Cantor).

have a look at this strange pic.
there's 2 circles.
a big one and a small one.

however, both circles consist of the same number of dots.
(there's a 1-1 correspondence.)
https://blog.wolframalpha.com/2010/09/10/transfinite-cardinal-arithmetic-with-wolframalpha/

is such a strange thing.
the whole and part can be the same size.¹
cf.
• Galileo's paradox.

¹ contrary to Euclid's 5th Common Notion (300 BC).
although some say that some CNs are by, e.g., Theon of Alexandria (4c).

mathematically, the answer is A
they're the same.
(even tho evens are part of integers.)

this is bc one integer corresponds to one even.
1 ↦ 2
2 ↦ 4
3 ↦ 6
4 ↦ 8
5 ↦ 10
︙
n ↦ 2n
︙

A) same bc they're infinite
B) infinity can't be compared
C) integers ofc bc evens are only half of them