Questions tagged [rational-numbers]

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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relation between rational and irrational, non-transcendental numbers?

a long time ago, when watching a video about continued fractions, I saw something interesting, all continued fractions in that video (all that were non-transcendental) had a rational-looking fraction. ...
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How to express it as a rational number [on hold]

Evaluate ((((3^2)^3)^1/3)^5)^−3/5) and express it as a rational number in lowest terms, as above. $${3^{{{2^3}^\frac13}^ 5}}^{-\frac35}$$
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The smallest positive integer vector from a positive rational vector

Suppose $\mathbf{q} = \left[\begin{array}{cccc}q_1 & q_2& \dots &q_n\end{array}\right]\in \mathbb{Q}_{>0}^n$ is a vector of positive rational numbers with relatively prime numerator and ...
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Constructing a non-empty perfect set of real numbers that does not contain rationals.

Duplicate: Perfect set without rationals My approach: We consider the set $[e, \pi]$. I am trying to "cover" the rationals by enclosing each one of them by open intervals with irrational endpoints, ...
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Is $z=e^{\frac{1}{\log(x)}}$ a solution to a polynomial?

Is $z=e^{\frac{1}{\log(x)}}$ a solution to a polynomial? $x\in\Bbb Q~\cap(0,1).$ Wolfram is telling me $z$ is algebraic but I'm not sure that I believe this. I believe it would follow from Schanuel'...
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Is even divided by even a rational or irrational number? [closed]

For any rational number, $\frac{p}{q}$ , $p$ and $q$ should be integers, $q\neq0$ and $p,q$ should not have any common factors. Now, if we have two even numbers, say $2m$ and $2n$ where $m$ and $n$ ...
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Rational topological basis for Euclidean topology - topology without tears 2.2.3

Context: self-studying topology without tears, now at question 2.2.3. Question: Let $\mathcal{B}$ be the collection of all open intervals $(a,b) \in \mathbb{R}$ with $a \lt b$ and $a, b$ rational ...
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Collection of intervals covers $[0,1]$?

For each $n=1,2,3,...$ and each $m=0,1,2,...,n-1$, let $$K^n_m = \left[ \frac{3m-n+1}{n} , \frac{3m-n+2}{n} \right] \subset (-1,2).$$ I am struggling these with two questions for quite some time: (...
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