Here’s a sample problem from discrete math when I took it in university:

For any integer n ≥ 0, let Cn be the set of all integer compositions of n with odd number of parts, and each part is congruent to 1 modulo 3. Prove that:

    |Cn| = [x^n] (x - x^4)/(1 - x^2 - 2x^3 + x^6)

Where [x^n] indicates the coefficient of the x^n term in the formal power series generated by the rational function (rational representation of the ordinary generating function).

I doubt many elementary school students would be able to solve problems like this.

Why not? All that is really required is knowing 1/(1-x) = 1+x+x^2+... and a bit of algebraic manipulation.

And the idea of a formal power series. And integer compositions. And combinatorial enumeration (counting sets in different ways for a proof). And a bit of set theory (cardinality of sets).

There is a whole lot of background stuff here that elementary school students do not have. Way more than what you’ve stated.

You definitely don't need to know any of that background to be able to arrive at the answer. To fully understand everything maybe, but all it takes is:

a = x^1 + x^4 + x^7 + ... = x(1 + x^3 + x^6 + ...) = x/(1-x^3)

a + a^3 + a^5 + ... = a(1 + a^2 + a^4 + ...) = a/(1-a^2)

Substitute + simplify. I don't think this is beyond a (fairly smart) elementary school student.

The question doesn’t ask for an answer, it asks for a proof. You can’t just write a bunch of algebra and call it a day. You have to justify all of your arguments.

There aren't really any complicated arguments being made, so I don't think a proof would be that involved.

On the other hand, all the analysis really boils down to exploiting continuity and smoothness of functions. Once you get that, the epsilon-delta formulation becomes really obvious. And then you just keep building on top of it, adding layers and layers of abstraction, just like with programming.

With discrete math, there are really no unifying themes.

I think of these with analogues with pixel rendering in order to understand integration and diferentiation on an intuitive way.

Once you 'see' how triangles/slopes are drawn on a GB/GBA, you begin to understand limits.

derivative of x^2 = 2x and a neglibile pixel/point that shouldn't be there but it 'exists' to show a changing factor.

I would expect people to be more comfortable with discrete math, because we are more used to thinking of separate things as opposed to things without a boundry, so to say. There are exceptions to the latter, of course, like air, warmth, rain, etc.