Between any two natural numbers, there is one natural number.
Step 1: Recall what natural numbers are.
Natural numbers are 1, 2, 3, 4, \(\dots\)
Step 2: Test with two consecutive natural numbers.
Take \(2\) and \(3\).
Numbers “between” them satisfy \(2 < x < 3\).
There is no natural number \(x\) with \(2 < x < 3\).
So, the claim fails for this pair.
Step 3: Test with two non-consecutive natural numbers.
Take \(2\) and \(5\).
Numbers between them satisfy \(2 < x < 5\).
The natural numbers here are \(3\) and \(4\) — that is two numbers, not one.
Step 4: Conclusion.
We found a pair (\(2,3\)) with none between, and a pair (\(2,5\)) with more than one between.
Therefore, the statement “Between any two natural numbers, there is one natural number” is false.
Note: The idea “there is always a number between two numbers” is true for rational numbers, but not for natural numbers.