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Since nobody ever showed which x is such that x^{2}=2

I confidently fumble on and say:

α=sup{x∈R: x^{2}<2}

Show ∝∈R; ∝^{2}=2

I also say:

∝≠max

Also, I restrict:

∝^{2}not>2

∝^{2}not<2,

....and then,

I wake up and scream: "Can anyone go further?!"

Thank you.

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# ...they say it's very difficult to show what sqrt2 is...

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