Difference between
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Difference between "Show" and "Prove"

In many mathematics problems you see the phrase "prove that..." or "show that..." something is. What's the difference between these two phrases? Is "...

Published: Aug 29, 2026

The right way of proving LHS = RHS
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The right way of proving LHS = RHS

I'm currently brushing up on my math before heading back to school for my bachelor's and am practicing on some questions. Given the following eq...

Published: Aug 29, 2026

What does
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What does "with respect to x" mean when integrating?

When dealing with derivatives, "with respect to $x$" means we are observing how a small change in $x$ (the input) affects a change in $y$ (the o...

Published: Aug 29, 2026

How to find a normal vector on a surface from a point out of the surface?
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How to find a normal vector on a surface from a point out of the surface?

For example, if we consider a shape in 2D like a circle at center $(x_0,y_0)$ with radius R so the equation would be: $$f(x,y)=(x-x_0)^2+(y-y_0)^2-R^2$$ n...

Published: Aug 29, 2026

Find the least nonnegative residue
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Find the least nonnegative residue

Find the least nonnegative residue of $5^{18} \mod 11$. To do this I took $5^2 \equiv 3 \mod 11$. Then I did $(5^2)^5 \equiv 3^5 \mod 11$. And $3^5 \equiv...

Published: Aug 29, 2026

Determine whether the following statements are true or false, and then prove answers
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Determine whether the following statements are true or false, and then prove answers

Determine whether statement is true or false, and then prove answer. For all integers $a,b,c$: a) if $a|bc$ and gcd$(a,b) = 1$ then $a|c$ b) if $a|c$ and ...

Published: Aug 29, 2026

Finding the equation for a line tangent to a parametric curve
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Finding the equation for a line tangent to a parametric curve

I have the parametric equation $x = 2t - 1$ $y = 3t + 5$ $t = -1$ (defined as $t_0$) I am trying to find the line tangent to it. My book says if $x'(...

Published: Aug 29, 2026

Difference between horizontal and vertical line tests.
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Difference between horizontal and vertical line tests.

Trying to understand what the differnce is between a vertical and horizontal line test. If an equation fails the vertical line test, what does that tell y...

Published: Aug 29, 2026

Integrating $\sec^2 x$ from first principles
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Integrating $\sec^2 x$ from first principles

Is it possible to solve $\int \sec^2 x ~dx$ without knowing that $\frac{d}{dx}\tan x = \sec^2 x$?

Published: Aug 29, 2026

Preparations for reading Algebraic Number Theory by Serge Lang
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Preparations for reading Algebraic Number Theory by Serge Lang

I am eager to learn algebraic number theory. It seems that Serge Lang's Algebraic Number Theory is one of the standard introductory texts (correct me...

Published: Aug 29, 2026

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