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In mathematics, a '''set function''' is a function whose input is a set. The output is usually a number.  Often the input is a set of [[real number]]s, a set of points in [[Euclidean space]], or a set of points in some [[measure space]].
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== Examples ==
 
Examples of set functions include:
* The function that assigns to each set its [[cardinality]], i.e. the number of members of the set, is a set function.
* The function
:: <math> d(A) = \lim_{n\to\infty} \frac{|A \cap \{1,\dots,n\}|}{n}, </math>
: assigning [[Schnirelmann density|densities]] to sufficiently [[well-behaved]] subsets ''A''&nbsp;⊆&nbsp;{1,&nbsp;2,&nbsp;3,&nbsp;...}, is a set function.
* The [[Lebesgue measure]] is a set function that assigns a non-negative real number to each set of real numbers. (Kolmogorov and Fomin 1975)
* A [[probability measure]] assigns a probability to each set in a [[sigma-algebra|σ-algebra]]. Specifically, the probability of the [[empty set]] is zero and the probability of the [[sample space]] is 1, with other sets given probabilities between 0 and&nbsp;1.
* A possibility measure assigns a number between zero and one to each set in the [[powerset]] of some given set. See [[Possibility theory]].
* A Random set is a set-valued [[random variable]]. See [[Random compact set]].
 
== References ==
* A.N. Kolmogorov and S.V. Fomin (1975), ''Introductory Real Analysis'', Dover. ISBN 0-486-61226-0
 
==Further reading==
* {{springer|title=Set function|id=S/s084730|last=Sobolev|first=V.I.}}
 
 
[[Category:Functions and mappings]]
[[Category:Basic concepts in set theory]]
 
 
 
{{mathlogic-stub}}

Latest revision as of 21:45, 26 August 2014

Unquestionably, it is very difficult to choose and decide on the apparent winner and minimize it to such a plain list as soon as one particular has gone through all the topmost potential kitchen knives set evaluations which includes Wusthof, Forschner Victorinox, Henckels, International, Shun, Chicago Cutlery, Minoso, Ginsu and a lot of extra. Specifically utilized for grilling so it should really be created of extended, wooden handles to shield hands and arms from as well substantially heat. Preferably, this should be made of non stick or stainless with aluminium core for speedy heat conduction. If you treasured this article so you would like to get more info about The Best Knife Set In The World i implore you to visit the page. Normally assume of investing on kitchen utensils that are tough and can last for years but not truly so high priced. Best Xacto Knife Set But thanks to their great skills, ceramic knives are not utilized in kitchens.

The disadvantage of the Japanese models is that they are a bit harder to sharpen, but some cooks really love the light weight and surgical precision of the Japanese scalpel sharp knives. This method of generating a knife is far more highly-priced, and only better knife manufacturers will use forging in production. The very best cutting edges are basically created with carbon steel, but this variety of blade does rust and discolor, and is not common or frequent as a result.

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For those of you that don't like silicone on your kitchen tools, these tongs are also obtainable entirely in stainless steel. One point I like about this utensil is that you can use it straight more than your pot or bowl although grating, as the legs have curves at the bottom, giving a safe match more than the rim of your pot or bowl. This is created of one single piece of 18/ten stainless steel, so it really is very sturdy and powerful in performing a good job.

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