Question

Transalate the following english statement into symbolic sentences with Quantifiers.
Between any integer and any larger integer, there is a real number.
The universe is Real numbers

Answer 1

\[\forall n,k\in\mathbb{Z} \;\;\;\exists x\in\mathbb{R} \;\;\;n<x<n+k\]

Answer 2

\[\forall a\in\mathbb{Z}\forall b\in\mathbb{Z}\exists c\in\mathbb{R} a<b\implies a<c<b\]

Answer 3

Yeah, either of those two will work.

Answer 4

yuppp ok ill medal nbouscal and nbouscal will medal king

Answer 5

Actually mine is a bit wrong. One second.

Answer 6

Oh, yeah it is. k could be negative.

Answer 7

\[\forall n\in\mathbb{Z}\;\;\;\forall k\in\mathbb{N} \;\;\;\exists x\in\mathbb{R} \;\;\;n<x<n+k\]

Answer 8

Thanks GUYS :)))))))