Question

\[\forall s, t \in \mathbb{R}\] with \[ s < t \exists n \in \mathbb{N} : s \leq n \leq t\]
false or true ?

Answer 1

take for instance s=0,3 t=0,6.
Can you find the value for n that those inequalities?

Answer 2

that satisfies*

Answer 3

yes for example 0,4 but its not equal to 0,3 and 0,6 so \[0,3\leq 0,4 \leq 0,6\] is false, right ?

Answer 4

\[n \in N\] so you can take only natural numbers (0,1,2,3,4,...)

Answer 5

aah sure so the answer of whole question is false right ?

Answer 6

0,4 must be equal or greater than 0,3, in this case 0,4 satisfies that inequalities but it's a real number, not natural

Answer 7

The answer is false because you cannot pick up any natural number that satisfies inequalities

Answer 8

ok thx satisfiying answer