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Cardinality of R and R^2

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How can I show that the cardinality of R and R^2, R=set of Real numbers, is equal.
I think by R^2 it is meant R x R, which means an ordered pair, am I right?

Is this possible just be showing that the first element in R^2 pair can be matched to R? But this is not necessarily a 'function' by definition, so there are infinite number of pairs with the same first element. How can you prove this?

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Solution Summary

A proof that R and R^2 have the same cardinality.

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Yes, R^2 means pairs of real numbers (x,y).

The idea is to "intertwine" the two reals into one, new, real number. This process can be repeated for any pair of reals, proving the one-to-one relation.

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