- #1
wellorderingp
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Can anyone help me prove the greatest integer function inequality-
n≤ x <n+1 for some x belongs to R and n is a unique integer
this is how I tried to prove it-
consider a set S of Real numbers which is bounded below
say min(S)=inf(S)=n so n≤x
by the property x<inf(S) + h we have x< n+1 for some h=1
thus we get n≤ x <n+1
Is this method correct? and can I use the archimedian property to prove the above,how?
n≤ x <n+1 for some x belongs to R and n is a unique integer
this is how I tried to prove it-
consider a set S of Real numbers which is bounded below
say min(S)=inf(S)=n so n≤x
by the property x<inf(S) + h we have x< n+1 for some h=1
thus we get n≤ x <n+1
Is this method correct? and can I use the archimedian property to prove the above,how?