Paradoxical Proof?

[BAndrew]

My point is there is no such thing as a "smallest" number that is measurable. We use negative infinity to approximate it because there is absolutely no way to know what it is, and infinity doesn't really mean anything on its own. Set theory is designed to work with finite numbers and the infinity abstract, but it doesn't take into account an infinitely small measurable number because it was not designed that way (and it is impossible). Therefore it is impossible to conclude there is definitely such a thing as a "smallest number" using a system that doesn't know what that is.

Wait. We are talking about Natural numbers.

This is the set
N{1,2,3,4,5.....} and maybe 0 depending on who you talk to.

No negative numbers are on this set and no irrationals (eg sqrt(2))


Note: The smallest Real number doesn't exist

Proof:

Spoiler below!

Let n the smallest real number
n-1 is a real number and smaller than n
contradiction

And that's why we use -∞