Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [real-numbers]

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

The field of real numbers, usually denoted by $\mathbb{R}$ or $\mathbf{R}$ is a field equipped with an order, which is complete with respect to that order. Moreover, it is the only ordered field which is complete (up to isomorphism). The real numbers are used as basis for measuring "length".

The real numbers can be classified in various ways: rational and irrational numbers; algebraic and transcendental numbers; computable and non-computable numbers; etc.

The real numbers carry a natural topology, which is generated by the order. The topology can be induced by a naturally arising complete metric. See more on Wikipedia.

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Prove that all numbers have a unique reciprocal

I'm learning logic for computer science and came across the question: If $\ n$ is a real number, $\frac{1}{n}$ is the reciprocal of $\ n$. Prove that all numbers have a unique reciprocal. I came up with the following method, but it seems so…
user395870
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How many digits are there before the hundredth $9$ in the following number: $97977977797777977777\cdots$

When I count from left of the following number, how many digits are there before the hundredth $9$: $$97977977797777977777\cdots$$ Before the 3rd $9$ there are $2$ sevens and before the 5th nine there are $4$ sevens... So basically there are $99$…
Justuraveragemathsstudent
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Cardinality of a set of real numbers

Is there a way to prove $|ℝ|=|P(\omega)|$? Will it help to show ℝ is uncountable?
tmac_balla
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Write in Interval Form

x² - 5x + 6 < 0 . x² - 2x - 3x + 6 < 0 . x (x-2) - 3 (x-2) < 0 . (x-3) (x-2) < 0 . x<2 & x<3 So is the Interval I=(-∞ , 3) Is this correct? can someone help?
user385779
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Intermediate value theorem to show real number solution

Use IVT to show there's a real number solution 1) sinx = x^2 - x - 1 where x ∈ ℝ (x is an arbitrary real number) 2) cosx = x^4 where x ∈ ℝ (x is an arbitrary real number) 3) ∜x = 1 - x where x ∈ ℝ (x is an arbitrary real…
Mike
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Show that if $a+b+c=0$ then $\frac{a^2+b^2+c^2}{2} * \frac{a^3+b^3+c^3}{3} = \frac{a^5+b^5+c^5}{5}$

Title says it all. It's my homework and I don't know where to start. A good hint would be appreciated.
Mislav Blažević
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Is there a $\lambda \in [0,1]$ so that $-\delta \leq \lambda a +(1-\lambda )b\leq \delta$?

Let $a<\delta$ and $-\delta 0$. Is there a $\lambda \in [0,1]$ so that $-\delta \leq \lambda a +(1-\lambda )b\leq \delta$?
M.Ramana
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When two values, $a$ and $b$, have the same value for their sum, product, and $a^b$...

For what values of $a$ and $b$ do the following three expressions assume the same value? $$a+b,\qquad ab, \qquad a^b$$ and what is that value? Clearly $\quad (a,b)=(2,2)\quad$ with a corresponding value of $4\quad$is one such answer. But I stumbled…
MaximusFastidiousIrreverence
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{x} = [x] - how many numbers?

{$x$} is like the fractional part: x - floor(x) $[x]$ is the whole part or whatever it's called: floor(x)
questionasker22
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Operation to remove powers of 10 from a number

I'm looking for the name of an operation that removes all powers of 10 from a number. For example if x=25673 then {x}=2.5673, or if y=0.0354 then {y}=3.54. Is there a name for this?
Stephen Peppin
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Degree of $\frac{1+\sqrt{2}+\sqrt{3}}{5}$

As title say, which is the degree of the algebraic number $\frac{1+\sqrt{2}+\sqrt{3}}{5}$ ? Obviously it is not degree 1 (rationals). It seems also not degree 2 (I do not known any way to convert form $\frac{a+b\sqrt{c}}{d}$).
pasaba por aqui
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More than Ten numbers in ten?

(I am going to be using the written out form of numbers seeing as the extra number im going to be talking about does not exist.) Ok. To start... What if there where Eleven numbers in Ten? For example (for the sake of not sounding stupid) it would…
T.Carter
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Value of $\sum\limits_{n=1}^{99}\frac{n}{1+n^2+n^4}$

Please help me out with this problem. $$\frac{1}{(1+1^2+1^4)} + \frac{2}{(1+2^2+2^4)} + \cdots+ \frac{99}{(1+99^2+99^4)}$$ lies between $(A)$ $0.46$ and $0.47$. $(B)$ $0.52$ and $1.0$. $(C)$ $0.48$ and $0.49$. $(D)$ $0.49$ and $0.50$. Explain the…
Ushosee
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Prove that ($\mathbb{R}$, $\le$) is a partial order

I was told that the relation $\le$ is a total order on R, it is dense, and it has a least upper bound property. I actually have don't understand those 3 properties... :/
David
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Please help, Prove Using Arithmetic Mean - Geometric Mean

Please help!! PROVE THAT f(x) = 2(1-x)(1+x) 1+x) ≤ 64/27 . and reaches maximum value for x ∈[0,1] off x=1/3 Can anyone tell me what the steps are, I just keep getting 4=4 whenever I try to solve it!
user135643
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