# A Lovely Riddle

Even though I'm closed in me, I love you.

I am entirely in you, even though I'm closed.

When I'm onto something, it's still me.

If it's you one by one, we're together.

No matter how I multiply, it's still me.

No matter how you multiply, it's still you.

If I am broken, I still love you.

So that we could find a point to fix me back.

What are we?

Subtle Hint:

I am after a common word. You are after a mathematician.

Moderate Hint:

The line of numbers is you, and also a broken me.

Decisive Hint:

• I was thinking the answer might be rot13(erny naq vzntvanel (1 naq v) be svavgr naq vasvavgr) but I have difficulty trying to form an explanation. Commented Feb 13, 2020 at 11:11
• @David I'm afraid those are not the answer. Should consider the moderate hint. Commented Feb 13, 2020 at 11:19

You are:

zero and one.

I am entirely in you, even though I'm closed.

Zero makes one when it's added to one.

When I'm onto something, it's still me.

Zero by another number makes zero.

If it's you one by one, we're together.

A bit contrived, but one divided into one makes one (one one) and 1+0=1.

No matter how I multiply, it's still me.

Zero always makes zero when it's multiplied by itself.

No matter how you multiply, it's still you.

Ditto for one.

If I am broken, I still love you.

So that we could find a point to fix me back.

If zero is divided into a number, it's still zero.

• Nice interpretion, but "we" are more advanced concepts. Hint: rot13("Jr" ner frgf bs cbvagf.) Commented Feb 11, 2020 at 12:14

Are you

a closed poset (partially ordered set) connected to its subset by a bijection?

Explanation:

Even though I'm closed in me, I love you.

love could mean the bijective relationship between these two sets in this context

I am entirely in you, even though I'm closed.

This can be a subset referring to its superset; both are closed sets

When I'm onto something, it's still me.

onto is a surjective relation

If it's you one by one, we're together.

This could mean one-to-one, an injective relation

No matter how I multiply, it's still me.

This could refer to a poset under a Cartesian product

No matter how you multiply, it's still you.

The superset of the poset referred here also follows the above property

If I am broken, I still love you.
So that we could find a point to fix me back.

This could refer to a transitive property that could connect two sets once they are split, although I am not entirely sure.

• Nice interpretion. Hint: "I" and "You" mean different notions. Commented Feb 11, 2020 at 8:54