TITLE: How can you disprove the statement $4=5$?
QUESTION [5 upvotes]: 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?

REPLY [3 votes]: From the point of view of a non-mathematician, but one who is forced to use some degree of logical and internally consistent thoughts, arguments, and communications with other humans on a daily basis, before proving any kind of relation between any two "objects", it is usually required that an agreement exists on what these objects are, or on what we agree ("rightly" or "wrongly") that they are. So I suggest that you and your friend sit down and agree on a common definition of what the visual symbol "$4$" means/represents, what the visual symbol "$5$" means/represents, and what the visual symbol "$=$" means/represents.  
After that, I feel that you will be able to debate more fruitfully whether the relation $4=5$ is valid or not, given your agreed upon definitions.  
As an example, just last night I agreed with a friend that "$4$" represents "moving away from the center of earth's gravity", "$5$" represents "hot chocolate" and "$=$" means "not the same thing". We also have reached agreement on the meaning of all words used in the above definition. Then we were able to reach the conclusion that $4=5$ is a useful compact expression of a relation that actually holds.