The Smallest Positive Number

Algebra Level 2

Is there a smallest real number greater than 0?

Yes, it exists No, it does not exist

View wiki
Ryan Lysafgt by ryan lysafgt , 18, United Kingdom

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Ryan Lysafgt
Sep 14, 2016

Answer is; It does not exist.
Proof by contradiction .

Assume the number p p is the smallest real positive number. Divide p p by 2. p / 2 p/2 is now even smaller than the smallest positive real number.

Contradiction! Hence p p cannot exist and there is no solution.

9 Helpful 0 Interesting 0 Brilliant 0 Confused

While the answer is correct (in that there is no REAL number like that). In some expanded systems there is a number defined to be the smallest number greater than 0 (as such it doesn't work in the same way as other numbers)

0 Helpful 0 Interesting 0 Brilliant 0 Confused

I don't claim to fully understand it but here is a link to the wikipedia page: https://en.wikipedia.org/wiki/Epsilon numbers (mathematics)

William Whitehouse - 4 years, 9 months ago

In some expanded systems

Can you elaborate on this?

Pi Han Goh - 4 years, 9 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...