# Questions tagged [real-numbers]

For questions about $\mathbb{R}$, the field of real numbers. Often used in conjunction with the real-analysis tag.

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### Why does there exist no real number such that it is equal to an integer multiple of any other number?

Was reading about waves in my Physics textbook and a mathematical fact was invoked which I was curious about: If we combine an infinitely large number of sinusoidal component waves, each with ...
• 145
1 vote
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### Set of numbers as a summation of two subsets

Denote by $\mathbb{F}$ one of the set of (all) integer, rational, real or complex numbers. We are looking for necessary and/or sufficient conditions for $\emptyset\neq C\subseteq \mathbb{F}$ such that ...
• 2,173
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### Intervals $( +\infty , - \infty ) = \mathbb R$

In intervals we say $( +\infty , - \infty ) = \mathbb R$. In this case what about zero because it is neither positive not negative
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### How do you solve $a^2b^2c-8abc+c^2+ac+bc-ab+8c+8=0$?

What is the general solution inf $\mathbb{R}_+$ of $a^2b^2c-8abc+c^2+ac+bc-ab+8c+8=0$, where $0<ab<8$? I can see the trivial solution 2,2,2, but what is the easiest way to write down the general ...
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### Relation between connectedness and Dedekind Completeness

In my calc class we constructed the real numbers using the following 5 axioms: The set is nonempty. The set has an ordering. The set has no first/last point. The set is connected. The set contains a ...
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### What is an example of a nonempty subset of $\mathbb{R}$ that is bounded above that does not contain its least upper bound?
What is an example of a nonempty subset of $\mathbb{R}$ that is bounded above that does not contain its least upper bound? This is an on-a-review sheet for my final. I thought the completeness axiom ...