I am wondering how I can prove that the closure of irrationals are reals. It is intuitively and logically sensible since irrationals and rationals are dense everywhere; thus, taking the closure of irrationals means it is also reals containing the irrationals. But how can I put this into a rigorous mathematical proof?
2026-03-31 18:42:31.1774982551
Rigorous proof of the closure of irrational numbers are reals
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