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- Dictionaryarbitrary/ˈɑːbɪt(rə)ri/
adjective
- 1. based on random choice or personal whim, rather than any reason or system: "an arbitrary decision" Similar Opposite
- 2. (of power or a ruling body) unrestrained and autocratic in the use of authority: "a country under arbitrary government" Similar Opposite
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Arbitrary means "undetermined; not assigned a specific value." For example, the statement x + x = 2x x + x = 2 x is true for arbitrary values of x ∈R x ∈ R, but the statement x + x = 2 x + x = 2 is not true for arbitrary values of x x (only for a specific value: x = 1 x = 1). Think of arbitrary as meaning the same as any.
Dec 22, 2018 · 5. "Arbitrary" basically means "any". So if we say something like "let n n be an arbitrary integer", you can think of this as "let n n be any integer". – pwerth. Dec 17, 2018 at 18:50. The way I explain it to my students, for example: "Let k k be an arbitrary positive integer.
I am writing a proof, which uses functions that can handle an arbitrary number of parameters like summing, or averaging.
2. Arbitrary means you can have any indexed union of sets. Finite means you can have only a finite union, i.e., you can only have an union indexed by a set of same cardinality of In I n, where In:= {1,..., n} I n:= {1,..., n} For example: Define Aα:= [1 α, 1] A α:= [1 α, 1] for every α ∈ [1, ∞) α ∈ [1, ∞)
Jun 17, 2018 · While trying to understand set theory from categorical perspective i.e. elementary theory of category of sets (Thanks to Lawvere), I am confronted with the situation where I need to construct arbitrary functions between two sets. Up until now following axioms are considered: $\exists $ terminal object $1$. $\exists$ initial object $0$.
17. When you encounter the term "arbitrary", it usually just means that a given statement is specified for any element from a given set of elments. For example, if I say, let x x be an arbitrary element of the interval [0, 1] [0, 1] I just mean that x x can take on any value within that interval. The term fixed connotes a similar but more ...
Dec 5, 2015 · 2. Arbitrary means arbitrary. That means that we put no restrictions on the number, but still each number is finite and has finite length. This means that we a priori can't assume that it has less than, say 1234 1234 digits. All we can know is that if we start in one end it and step through we will eventually reach the other end.
In basic topology of real number ( real analysis) , there is these two theorems which states : The union of arbitrary collection of open sets is open. Another one is : The intersection of finite collection of open sets is open. Here, I would like to ask what is the difference between arbitrary and finite ?
Feb 16, 2016 · In contrast, it is more meaningful to define $\exp$ as motivated by the defining differential equation, and define $\ln$ as an 'inverse'. $\endgroup$ – user21820 Commented Feb 17, 2016 at 7:23
Jan 5, 2021 · The term "arbitrary" generally means "done without any reasoning or logic". So when a mathematician says "Let x x be an arbitrary integer", they are saying "Let x x be an integer, where the integer is chosen without any reasoning or logic". Because the integer is chosen withou any reasoning, it is unknown / unspecified.
