Prove that there is an one-to-one function from $\mathbb R × \mathbb R$ to $\mathbb R$

Question

I am not sure how this would work, since any solution I think of results in a mess of over complicated rules.

Thank you in advance!

I'm assuming it is $\mathbb{R}$. See https://math.stackexchange.com/questions/197735/injective-function-from-mathbbr2-to-mathbbr — K. Y, Oct 01 '18 at 02:42

score 0 · Accepted Answer · answered Oct 01 '18 at 06:09

0

Show equivalently (0,1) is equinumerous to (0,1)×(0,1).
Let a = $0.a_1,.. a_n,..$ and b = $0.b_1,.. b_n,..$ be the
decimal expansion of two numbers not ending with 999...
Map (a,b) to c = $0.a_1,b_1,.. a_n,b_n,..$
Show c does not end with 999...

answered Oct 01 '18 at 06:09

William Elliot

17,598

Prove that there is an one-to-one function from $\mathbb R × \mathbb R$ to $\mathbb R$

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