# Tagged Questions

Questions about numbers expressible as the quotient of two integers. For questions on determining whether a number is rational, use the (rationality-testing) tag instead.

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### A group automorphism of real numbers that is not the identity

Is it possible to have a group automorphism of the additive group of the real numbers that fixes a subset of real numbers but is not the identity? The subset might be infinite. I'm thinking of using ...
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### There is no smallest rational number greater than 2

I have a problem that I am seriously stuck on. I'm not sure what to do I've seen similar proofs online with the least positive rational number but this is apparently different and I'm not sure why. ...
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### How to find the closest bounded rational approximation to a rational number?

Say I have a rational number $a/b$ and I want to find its closest rational approximation $x/y$ where $$x_- \leq x \leq x_+$$ $$y_- \leq y \leq y_+$$ for some constants $x_\pm$, $y_\pm$. How can I ...
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### Number of ordered positive rationals (x,y,z) satisfying following conditions.

How many ordered triples $(x,y,z)$ of positive rational numbers satisfy the conditions: $x+y+z$, $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}$, and $xyz$ are all integers.
### proving $\sqrt 2 + \sqrt 3$ is irrational [duplicate]
I need to proof that $\sqrt{3} + \sqrt{2}$ is irrational, without using the fact that an irrational number plus a rational number equals irrational. also, i can't use the rational root theorem. that's ...