Induction

Probability Level 3

How many subsets $X \in \mathbb{Z}$ are there that satisfy the set equation

$X=X+1$ ?

Note: Basically the set equation means $\forall x \in X, x+1 \in X$

If that's too easy try this or maybe even this

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1 solution

Wen Z
Jul 27, 2016

$X=\phi$ and $X=\mathbb{Z}$

It can be shown that if $n \in \mathbb{Z}$ and $n \in X$ , then $\forall \space x \in \mathbb{Z} ,\space x \in X$ by a quick induction thing

I didnt understand it,is there a wiki for that?

Mr Yovan - 4 years, 10 months ago

Okay then so basically X=X+1 means that the sets X and (X+1 = x : x-1 is in X) are the same. Basically X+1 is just X except you add one to every element.

Wen Z - 4 years, 10 months ago

Induction

If that's too easy try this or maybe even this

1 solution

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