- #1

kingwinner

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**1) Find the cardnality of the set of continuous functions from R to R.**

Let's consider a simplified version: for the cardnality of the set of functions from R to R, I can compare it with the set of characteristic functions of subsets of R and conclude that they both have cardnality 2

^{c}

But when the word "continuous" is inserted, how can I find its cardnality?

Thanks for any help!