"Consider the two open intervals (0,2) = {x is an element of R such that 0 < x < 2} and {0, infinity)={x is an element of R such that 0 is less than x}, both of which are uncountable sets. Do these two sets have the same cardinality? Explain.
2026-03-24 23:42:46.1774395766
1:1 Matching with Uncountable Sets
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Yes. Use the function $\tan\big(\tfrac{\pi}{4}x\big)$ as your bijection between your two intervals.