Using definition of pre-image to prove $ X \subset f^{-1}(f(X)) $

Asked Jan 15 '16 at 20:06

Active Jan 16 '16 at 03:36

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I am trying to prove easy statements such as one listed here: http://mathworld.wolfram.com/Pre-Image.html

My attempt: let $ x \in X$ then $f(x) \in f(X)$ so $x \in f^{-1}(f(X))$ but I am not really doing anything but looking at the definitions - how may i formalise this?

edited Jan 16 '16 at 03:36

Andrés E. Caicedo

79,201

asked Jan 15 '16 at 20:06

settheory

3

You're ok. Indeed, it is a formal argument – sinbadh Jan 15 '16 at 20:09
That's formal enough. It is just a "definition chase" — that's why it's an easy statement! – BrianO Jan 15 '16 at 20:40

Using definition of pre-image to prove $ X \subset f^{-1}(f(X)) $

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