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Question 1: T/F: $\exists x\in(0,1] \forall y\in(0,1](x \leq y)$

My first assumption is this statement is true. However, I'm having trouble providing a sufficient proof since we cannot find the 'smallest number' next to 0.

Mel A.
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    Another way to read the statement is "does there exist some element $x$ in (0,1] such that for all y in (0,1] $x \leq y?$". – David Sep 26 '17 at 18:44

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In English, the question is, "does the interval $(0,1]$ have a smallest element? ". If $a\in(0,1]$ then surely $a/2\in(0,1]$ also?

Angina Seng
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