How can you disprove the statement $4=5$? I know this sounds insane. But bear with me, my friend said this to me with a straight face: 

Can you disprove the statement: $4=5$?

And I was like is that even a question, thats obvious, $5$ is $4+1$ and $5$ comes after $4$.
He was like: but you haven't still disproved my statement.
Something like this went for around 30 minutes...and he wasn't happy at the end at all
Is he correct? If not, how does one actually give a good sensible answer to such a person?

Subtract 4 from both sides of $4=5$, yielding $0=1$. Now $0$ is defined to be the number such that $0+x=x$ for every $x$ and $1$ the number such that $1\cdot x = x$ for every $x$. But with that definition of $0$ we get that $0\cdot x = (0+0)\cdot x = 0\cdot x + 0\cdot x$, so $0\cdot x =0$ for every $x$. So since $1$ is the multiplicative identity (the property described above), but $0$ behaves differently multiplicatively, they can't be equal. 
