So?

You surely are not suggesting that maths stops as soon as you have an inequality, are you?  :-)

You certainly can have deductive chains beginning with

Because X>Y,

Therefore ...

Right?

Or do I misunderstand you?

In my example we had:

Because 4>2

Therefore...

...

Therefore 2>4

Now, given that the "..." represented a chain of reasoning, try to work out what it might have been.

Also show where the chain of reasoning was wrong. We know that it is wrong, because it produced a false conclusion from true premises, but how?