Proof involving number theory

[courtrigrad]

Hello all

I need help with the following proofs

1. If x and y are arbitrary real numbers, prove that there is at least one real z satisfying x < z < y. (Do I just use the Archimedian Property?)

Thanks

[hypermorphism]

(Do I just use the Archimedian Property?)


Yep. :smile:

[matt grime]

No. and it isn't true as stated.

x and y must be distinct, and the requirement of being R is unnecessary, since it is true for Q (and C).


what is (x+y)/2?

[hypermorphism]

Good catch. I was thinking of rational numbers between arbitrary reals.