Prove that there is no greatest even integer (1 Viewer)

[SB257426]

Is this how I should complete my proof:

By way of contradiction assume that 2k is the largest even integer.

Now consider (2k)!

(2k)! = (2k)(2k-1)(2k-2).......(k)(k-1)(k-2)......(2)(1)

= 2[k(2k-1)(2k-2).......(k)(k-1)(k-2)......(2)(1)]

= 2p, which is also an even integer. This contradicts the fact that 2k was the largest even integer. Therefore it is sensible to claim that there is no even integer since 2p>2k

 

[tywebb]

If you assume if it exists then it is 2k for an integer k.

But then I'd be more inclined just to add 2.

So now 2k+2=2(k+1) is a bigger even integer - contradiction there is no biggest even integer.

 

[synthesisFR]

yeah just add 2 lmao