Are the subdivisions involved in an integral countably infinite or uncountably infinite? If they're countably infinite...

Are the subdivisions involved in an integral countably infinite or uncountably infinite? If they're countably infinite, then could you find a bijection between some any definite integral and some infinite series?

faceplam
>what are Riemann sums

Countably infinite. Yes.

Yes but Im not sure what it would apply to

uncountably infinite by definition.

...

That's only countably many, boyo.

It would allow you to kinda "stretch" a definite integral out over the naturals. Not sure what the purpose would be, but I find it fascinating.

they are finite.

it's a limit n to infinity, where for every n, you have finitely many

just like in

[math] \sum_{n=1}^m \dfrac{1}{n^2} [/math]

you have always finitely many (rational) terms, while

[math] \lim_{m\to \infty} \sum_{n=1}^m \dfrac{1}{n^2} = \dfrac{\pi}{6} [/math]