Questions tagged [binary-operations]
A binary operation on a set $X$ is a map $\ast : X \times X \to X$. Usually, we denote $\ast(x, y)$ by $x\ast y$. For questions about operations in binary arithmetic (base 2), use the tag (binary) instead.
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View minus sign as operator or part of the number? How to differentiate?
I came across this problem,looking at the distributive law "a*(b+c) = ab+ac" / "a*(b-c) = ab-ac".
Lets say we have the following term: -4 * (2 - 4)
What would you say is c? Is c -4 ...
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How to deal with multiple plus-or-minus signs (±) in a single expression
When you have a single plus-or-minus symbol, the meaning is clear:
$a±b = (a+b) OR (a-b)$
When you have plus-or-minus and minus-or-plus symbols, the meaning is also clear, as described in many places, ...
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priority of operations in function composition is backwards
I feel like the priority of function composition is backwards, and I would like to have a deep understanding of the phenomenon.
I do understand that function composition reads right to left:
$$(f\circ ...
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Ranking and unranking of a binary subset
Let's consider "N" bits.
We want to rank and unrank a specific subset of bit combinations based on the following criteria -
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Could we define a fifth arithmetic operation on real (or complex) numbers that is independent of addition, subtraction, multiplication, and division?
The four basic arithmetic operations with real (or complex) numbers are addition, subtraction, multiplication, and division. the first two being inverse operations and the last two being inverses of ...
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Classification of binary associative operations on $\mathbb{R}^n$
Is there an explicit characterization of associative binary operations on two vectors of the same dimension?
Some examples include component wise +/*/max, or matrix multiplication if the vectors can ...
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Problem about binary/decimal bitwise and operation
I found a (maybe) fun problem, but I could not solve this.
$10110_{(10)} \& 10011_{(10)} = 10010_{(10)}$
$10110_{(2)} \& 10011_{(2)} = 10010_{(2)}$
$\&$ is the bitwise and operator.
Their ...
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Problem 27. Integrate a conditional BITWISE right-shift function.
This problem has been haunting me since I've seen it on Facebook.
The function $f$ converts $1$s into $01$s when written in binary, e.g.,
when $a = 0.101$_bin, $f(a) = 0.01001$_bin.
Compute the ...
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The operation $ (a,b)(c,d)=(ac-bd,ad+bc) $ on $\Bbb R\times\Bbb R\backslash (0,0)$ yields a group
Here is the binary operation $ *: \mathbb{R}\times \mathbb{R} \backslash (0,0) $ defined by $ (a,b)(c,d)=(ac-bd,ad+bc) $. My idea is that to show this is a group ($\mathbb{R}\times \mathbb{R} \...
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Why do k arithmetic right/left bit shifts divide by $2^k$/multiply by $2^k$ in two's complement, rigorously?
I want to understand the semantics of rights bit shifts x>>k in two's complement properly, in particular why do right bit shifts of size $k$ approximately ...
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Which of the following is a binary operation?
This question was asked to me by a student of mine and I am not able to make any progress on this question.
Let $A=${1,2,3,4,5} , then which of the following is a binary operation?
(a) {((1,1),1),((...
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What do the symbols for these binary operations on a set mean?
If S = {0,1,2,3,4} and (a,b) is an arbitrary ordered pair such that a ∈ S and b ∈ S, which of the matchings in Exercises 12-15 are binary operations on S? Construct operation tables.
(a,b) ----> a ...
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Is a commutative and associative with neutral element operation and inverses on R^2 necessarily componentwise sum?
I'm trying to make a derivation of the standard operations of complex numbers from field axioms and the condition that operations on real numbers work the same way. One part of that work is proving ...
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Binary operator and their inverses.
Having trouble finding it, but there was a question posted last week regarding a binary operation $x,y \in \mathbb R, x\oplus y=\frac{xy}{x+y}$. It also addressed Resistors in parallel and worked ...
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Operation that is distributive over convolution of integer sequences
I'm working in the spaces $\mathbb{I}_Z$ and $\mathbb{I}_Q$ of infinite integer/rational sequences that start with $1$:
$$∀x∈\mathbb{I}_Z\ ∀n∈\mathbb{N}:x_0=1,x_n∈\mathbb{Z}$$
$$∀y∈\mathbb{I}_Q\ ∀n∈\...
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