Discrete Math Question (Urgent)

Question

Let n ∈ ω. Suppose that f : n → A is onto A. Prove that A is finite.

Answer 1

The function F is on .

it means the element of B has a distnict & unique preimage on A.

And given that set A is finete.

Where we know that A has finite no of elements. Which are the distinct preimage of B.

So we from the given condition we know that B is also finite.

Proof:

Given that F is on to

It implies that there exist distinct & unique element bi which belongs to B

F is a function it means that every element of A has a image in B.

Which show |A|《 |B|......(.1)

But given that F is on to which means

|A|》|B|........(2)

from 1 & 2 we can say that

|A|=|B|

A is finite . So B is finte. (Proved)

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