This is the property shared by many binary operations including group operations. For a binary operation $\cdot$, associativity holds if $(x\cdot y)\cdot z = x \cdot(y\cdot z)$.

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tax and discount problem

Problem : In the total purchase amount $z, x\%$ is tax and $y\%$ is discount. Even if the tax is applied first and then discount or if discount is applied and then tax, the final amount is always ...
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Proof of The Associative Law and The Commutative Law.

The associative law of multiplication for three positive integers $a,b$ and $c$ can be proved$^1$ from the Commutative Law and the property of "Number of things" easily. We can prove$^2$ the ...
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Can we have an associative form of “octonions” and hypercomplexes, if we eliminate division?

I'm interested in hypercomplexes, or number systems with many square roots of $-1$. Now, I know that quaternions are non-commutative, but associative. I'm wondering if it's possible to have a number ...
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Why are exponents not associative?

I ran into something that seemed odd to me today: exponents are not associative. The following equation sums that up: $$ 10 * 2^{5x} \not\equiv 20^{5x} $$ Why is this the case? Is there some ...
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Does associativity justify $(f^{-1}gf)(f^{-1}hf) = f^{-1}gff^{-1}hf$?

I'm self-studying abstract algabra (Herstein) and while working on an easy problem became uneasy with a step in my derivation. Given the symmetric group $S_n$ whose elements are bijections $f: S \to ...
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Splitting up bracket terms

I found a statement saying: Let $\circledast $ be an associative binary operation on a set $\mathbb{X}$. A bracket term of length n, consisting of n elements $a_1, ..., a_n$ and arbitrary brackets, ...
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Is convolution associative with regards to the complex unity?

Setup: I need to do a convolution with the function $\cfrac{i}{x}$, and I would like to get rid of the $i$. My functions to be convolved are all real valued. According to the ever-failable wikipedia, ...
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How to correctly do a division using a slash?

What's the correct way to do division using a backslash? If I write $a/bc + d$, will that be equal to $(a/(bc))+d$? Basically, if I place a slash, will I divide by what's directly behind the slash ...
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Real life examples of commutative but non-associative operations

I've been trying to find ways to explain to people why associativity is important. Subtraction is a good example of something that isn't associative, but it is not commutative. So the best I could ...