Hi there,

I've started reading the book, "A concise introduction to pure mathematics", which I'm finding a great read so far. I'm on the first chapter on sets and proofs, and have come across the following example:

Prove that

The author goes on to give a non-proof:

Why is this a non-proof? I'm not sure I understand fully? He says that we have shown that if P is the statement we want to prove, and Q is the statement that 48 < 49, then P implies Q; but this tells us nothing about the truth or otherwise of P.

Instead, he says the correct way to prove the above is method by contradiction, as follows:

which is obviously a contradiction, but I don't understand why the first method (the non-proof) isn't actually a proof itself?

Hope someone can help explain this to me, thanks!