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## Main Question or Discussion Point

I have learnt that integral is the Riemann sum of infinite rectangle, that:

Ʃ[itex]^{n=1}_{∞}[/itex]f(x

However, I think that (a,b) is the continuous interval, so the number of rectangle should be

So I wonder whether there are some problem that this definition is not valid anymore.

Ʃ[itex]^{n=1}_{∞}[/itex]f(x

_{i})Δx_{i}= ∫[itex]^{b}_{a}[/itex]f(x)dxHowever, I think that (a,b) is the continuous interval, so the number of rectangle should be

**c**instead of [itex]\aleph[/itex]_{0}(cardinality of natural number**N**).So I wonder whether there are some problem that this definition is not valid anymore.