You and You Only

[YourLooks]

x is a real number, could you tell me how to prove that there will always be one and only one positive integer m such that m=< x <m+1 and one and only one positive integer n such that n< x =< n+1 ?
Thank you.....

[jcsd]

Looks like homework, read the rules on homework above (we'll help you, but we won't do it for you).

[YourLooks]

Oh, Poet jcsd, I didn't know that.
But how will Poet help me ?

[newPatrick]

x is a real number, could you tell me how to prove that there will always be one and only one positive integer m such that m=< x <m+1 and one and only one positive integer n such that n< x =< n+1 ?
Thank you.....
Suppose there are 2 sets X and Y, X={k belongs to Z : k<x}, Y={k belongs to Z : k<=x}, which means X and Y are not set zero and there should be a sup. Now you only need to let m=supX and n=supY then try to prove m belongs to X and n belongs to Y. Thats all.

[YourLooks]

Thank you for helping Yourlooks, you are really new to this forum :wink: