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Continuous Real Functions and Subrings

Let R be the ring of continuous functions from the reals to the reals. Define A={f in R: f(0) is an even integer}. Show that A is a subring of R, but not an ideal.

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Continuous real functions and subrings are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.