# Tagged Questions

Questions on basic arithmetic involving numerical quantities only. Questions involving variable values (other than the result of the operation) should be placed under the (algebra-precalculus) tag.

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### “there exists” and “for some” are the same, right?

I think "there exists" and "for some" are the same, but still want to make sure. Ex: $x > ky$ for some k or there exists a k such that $x > ky$
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### Arithmetic and geometric sequence

Which two numbers should be placed between -5 and 49 so that the first three numbers form an arithmetic sequence, whereas the last three numbers form a geometric sequence?
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### Check algebraic transformation with trial numbers?

I did some algebraic transformations on equations with multiple real variables $x_i$, and I'd like to check whether the transformed equation is still valid. The equations are basically only rational ...
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### Order of parsing + and -

This seems like an absurdly simply question, and is possibly below the level of this forum, but it seems the most sensible place. I'm building an arithmetic equation parser, and currently working on ...
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### When is $\sqrt{a^2}=\pm a$ and when is $\sqrt{a^2}=a$?

When we derive some formula and have to do huge algebraic expansions that deal with raising powers we use exponent rules mindlessly and we never write down the $\pm$ symbol. Why is this right? My ...
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### 2+2=square root of 16. What's the appropriate answer? [closed]

4? Positive and negative 4? I just got into an argument with a buddy about this. He argues if it's not an i, it's not included as a imaginary number, but only the real positive number.
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### What would Gauss do in this case: adding $1+\frac12+\frac13+\frac14+ \dots +\frac1{100}$?

We all know the story related to Gauss that Gauss' class was asked to find the sum of the numbers from $1$ to $100$ as a "busy work" problem and and he came up with $5050$ in less than a minute. He ...
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### Take $\sqrt[n]{m}$ where $n$ is a positive non-integer number. Is this possible?

The title pretty much says it all. I am trying to figure out how to take the $n$-th root of a number $m$ where $n$ is a fractional number. Unfortunately all I could turn up on Google was how to take a ...
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### If $ab(a+b)=2$ then what will be the value of $\frac{1}{(ab)^3}-a^3-b^3$?

The question given is, If $ab(a+b)=2$ then show that $\dfrac{1}{(ab)^3}-a^3-b^3=?$ $(a)\ \ \ \ \ 0$ $(b)\ \ \ \ \ 1$ $(c)\ \ \ \ \ 3$ $(d)-1$ I noted that $a=1$ and $b=1$ satisfy the ...
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### Using alternate order of operations

Let's pretend, for a second, that we used PEASMD instead of PEMDAS. That is, addition/subtraction and multiplication/division are switched. Is it possible to write: $$(a\times b)+c$$ without ...
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### How to calculate fuel cost and mpg?

A car has a mileage of "5 miles per litre" and traveled a distance of 573 miles. The cost of fuel is £1.09 per litre. How do I compute the miles per gallon(mpg) and the total cost of fuel for the ...
While fooling around on my calculator I found: $$7^4 + 8^4 + (7 + 8)^4 = 2 * 13^4$$ $$11^4 + 24^4 + (11 + 24)^4 = 2 * 31^4$$ I'm intrigued but I can't explain why these two equations are true. Are ...