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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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8. 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. So you get ...
Feb 19, 2013 · 10. The meaning is totally different. The statement "for arbitrary x x " means "for all x x ", whereas "finite" is a term that can be applied to a set to indicate that its cardinality (size) is a natural number. In particular, asking "is A A arbitrary" only makes sense in certain contexts, where you may be asking whether something is being ...
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.
Jun 17, 2020 · 1. "Arbitrary union" essentially means that there are no limitations. We might specify in other cases that something is true for only finitely or countably many iterations of that operation, particularly in topology for instance, but arbitrary - as in "arbitrarily many" - means it holds no matter how many: finite, countable, uncountable...
Sep 16, 2020 · 1. If a property P is true "for some arbitrary element" in a given set, then that will be true "for all" the elements in the set and vice-versa, so they are identical in the sense that they convey the same meaning. Now let's say someone told you that property P is true for some set A. well what will you do to prove him wrong, just find some ...
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
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 $0$.
Mar 22, 2014 · With the definition over arbitrary angles we get just a way, a rule which can given input transform to some output. But that doesn't mean anything. When we have a right triangle, we can clearly see what sine means and that is a ratio. When we define it for arbitrary angles we just get a pair of values. The first number is the input to the sine ...
Mar 5, 2013 · 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 ?
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 ...
