An algebra problem by Mehul Kumar

Algebra Level 4

Define f : N → R f: \mathbb N \to \mathbb R such as f ( x ) = sin ⁡ ( x ) f(x)=\sin(x) .

What is the cardinality of the range?

Finite same as size of R same as size of Z none of these

Mehul Kumar by Mehul Kumar , 23, India

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1 solution

Cardinality of Range of given function is countably infinite. We know cardinality of R \mathbb R is uncountable, so this can't be range of given function. Though the finite set is countable but not, countably infinite. The integers is countably infinite, so the range of given function is Z \mathbb Z

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But you also need to show it not finite.

Mehul Kumar - 3 years, 5 months ago

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