Theorem nnge2recfl0

Description: The floor of the reciprocal of an integer greater than 1 is 0. (Contributed by AV, 10-Apr-2026)

	Ref	Expression
Assertion	nnge2recfl0	⊢ ( 𝑁 ∈ ( ℤ≥ ‘ 2 ) → ( ⌊ ‘ ( 1 / 𝑁 ) ) = 0 )

Proof

Step	Hyp	Ref	Expression
1		nnge2recico01	⊢ ( 𝑁 ∈ ( ℤ≥ ‘ 2 ) → ( 1 / 𝑁 ) ∈ ( 0 [,) 1 ) )
2		ico01fl0	⊢ ( ( 1 / 𝑁 ) ∈ ( 0 [,) 1 ) → ( ⌊ ‘ ( 1 / 𝑁 ) ) = 0 )
3	1 2	syl	⊢ ( 𝑁 ∈ ( ℤ≥ ‘ 2 ) → ( ⌊ ‘ ( 1 / 𝑁 ) ) = 0 )