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Akhil showed that the Cardinality of set of real continuous functions is the same as the continuum, using as a step the observation that continuous functions that agree at rational points must agree everywhere, since the rationals are dense in the reals.

This isn't an obvious step, so why is it true?

Akhil showed that the Cardinality of set of real continuous functions is the same as the continuum, using as a step the observation that continuous functions that agree at rational points must agree everywhere, since the rationals are dense in the reals.

This isn't an obvious step, so why is it true?

Akhil showed that the Cardinality of set of real continuous functions is the same as the continuum, using as a step the observation that functions that agree at rational points must agree everywhere, since the rationals are dense in the reals.

This isn't an obvious step, so why is it true?

Akhil showed that the Cardinality of set of real continuous functions is the same as the continuum, using as a step the observation that continuous functions that agree at rational points must agree everywhere, since the rationals are dense in the reals.

This isn't an obvious step, so why is it true?

This is a step needed in the proof Akhil gave that the Cardinality of set of real continuous functions is the same as the continuum.

Akhil showed that the Cardinality of set of real continuous functions is the same as the continuum, using as a step the observation that functions that agree at rational points must agree everywhere, since the rationals are dense in the reals.

This isn't an obvious step, so why is it true?