Proving there exist unique integers m and n bounding a real number x

YourLooks · Sep 28, 2004

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 · Sep 28, 2004

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

YourLooks · Sep 28, 2004

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

newPatrick · Sep 29, 2004

YourLooks said:

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 · Sep 30, 2004

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

Proving there exist unique integers m and n bounding a real number x

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