Bijection from $\mathcal{P} (\mathbb{R})$ to the set of functions from $\mathbb{R}$ to $\mathbb{R}$

Asked Apr 03 '22 at 15:21

Active Apr 03 '22 at 15:21

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I’m a bit confused as to how we get the bijection between a powerset of a set to the set of functions from that self to itself

I can see the obvious bijection from the powerset to the set ${[0,1]}^{R}$, but I’m missing the bijection from the set of these binary functions to the set of all real-valued functions

asked Apr 03 '22 at 15:21

Ablation_nation

https://math.stackexchange.com/questions/20016/bijection-between-2-mathbb-r-and-mathbb-r-r?rq=1. – Vivaan Daga Apr 03 '22 at 15:29
Thanks so much both of you - yes I somehow totally missed that one when searching, my bad. Thanks for the link! – Ablation_nation Apr 03 '22 at 19:16

Bijection from $\mathcal{P} (\mathbb{R})$ to the set of functions from $\mathbb{R}$ to $\mathbb{R}$

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