This question is a question in my textbook, and I cannot stop thinking about it. The question: Is $\pi$ even or odd? I don't know if even or odd is defined for decimals or for irrational numbers, or if it is, how to find whether $\pi$ is even or odd. Can somebody help?
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1Neither of them... – mrtaurho Apr 27 '19 at 16:59
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6*Which* textbook? – José Carlos Santos Apr 27 '19 at 17:00
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Even if the last digit decides whether a non-integer is even or odd, we cannot answer the question because $\pi$ has no last digit. – Peter Apr 28 '19 at 07:50
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Even numbers and odd numbers are defined only for integers, as an integer is even when it is of form $2k$, where $k$ is an integer, an integer is odd when it is of form $2p+1$, where $p$ is an integer. But $\pi$ is irrational(in fact transcedental). So there is no way of this.
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2Not true. In fact parity is well defined for may rings of (irrational) algebraic integers, including Gaussian integers $\,\Bbb Z[i],\,$ e.g. [see here.](https://math.stackexchange.com/a/26843/242) – Bill Dubuque Apr 27 '19 at 17:05
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1OP said nothing of the sort, and many of the rings I mention (enjoying parity) are subrings of $\Bbb R.\ $ – Bill Dubuque Apr 27 '19 at 17:08
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1@user665856 So should we consider such a statement "$\pi$ is even" a false statement or meaningless? – user599310 Jul 28 '20 at 18:49