Question

please give me some examples for the closure property in this set:
The odd numbers is closed under multiplication.

Answer 1

take two general odd numbers , 2k+1 and 2n+1

(2k+1)(2n+1)

Answer 2

= 4kn + 2 (k+n ) + 1

= 4kn +2k +2n + 1
= 2 [ kn + k +n ] + 1

let kn +k +n = C ( another constant )

Answer 3

therefore (2k+1)(2n+1) = 2C +1 ( the general form of an odd number )

there

Answer 4

not an example, but a proof, good enough

Answer 5

made a mistake above

should be : 2 [ 2kn + k +n ] + 1

Answer 6

but the argument is the exact same, that expression in the bracket is a sum of constants, and can therefore be represented by a single constant.