Integrating is hard enough

Calculus Level 3

There are an uncountably infinite number of integrable functions, but there are also an uncountably infinite number of functions that are not integrable. Which are there more of?

Note : According to Cantor, infinite sets can have different cardinalities. The question asks which set has a larger cardinality.

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Impossible to determine Non-integrable functions Integrable functions Same number

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Trevor B. by Trevor B. , 22, USA

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1 solution

Gaurav Jain
Aug 8, 2015

I don't have a strong point to justify , but my perception was that out of the various permutations of the combination of funtions , composite functions , functional equations only a finite or small no of arrangements do make the resulting function defined while others have not well defined curves .... I need a feedback and discussion.

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Doesn't your argument shows the cardanalities to be the same as integrable functions?

Pi Han Goh - 5 years, 10 months ago

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I think it's because non-integrable functions can exist within the space of both linear and nonlinear transformations while integrable functions only exist within the space of linear transformations.?Therefore the two classes of functions do not have the same cardinality? This is assuming you're talking about Riemann Integrability which should be specified in the question. Just a guess though.

Adrian Castro - 5 years, 10 months ago

What about you @Ronak Agarwal ? Please suggest..

Gaurav Jain - 5 years, 10 months ago

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