Is this equality [0.5, 7.5] ∩ N = [1, 7] correct?

Question

A brief explanation would be greatly appreciated!

Answer 1

N = set of natural (counting) numbers = {1, 2, 3, ...}

So, the set N∩[0.5, 7.5] = the set of all counting numbers that lie between 0.5 and 7.5.

= {1, 2, 3, 4, 5, 6, 7}, which is not the same as the interval [1,7].

Therefore, the given statement is false.