Examples of set functions - Mathematics Stack Exchange
A function that assigns the integer n to a set if the set can be out in one-to-one correspondence with the set of integers {1,2,3...n}. This is similar to the "cardinality" function, but as it stands it only works for finite sets.
What is the set-theoretic definition of a function?
$\begingroup$ @grautur: The problem is that of proving that a function exists from $\mathbb{N}$ to the set of all socks in the pairs with the desired properties. AoC is required to be able to write down a proof that such a function exists. Again: it's subtle, and it is connected to infinity in some sense, but not simply in the sense of "naming".
elementary set theory - In what manner are functions sets ...
2013年9月1日 · Take the function that maps a set to its singleton. The ordered pairs $(x, \{x\})$ are too many to form a set. If a function is too big to have a corresponding set, it can't be that set. Most importantly, it would be a type confusion to identify a function with an object like a set. A function maps some object(s) to an object.
How can a function be a set? - Mathematics Stack Exchange
2022年4月3日 · Function is a rule. Set is just a collection. How does the intuition of function connect to the set theoritic definition of function? Apologies if I sound like a overthinker. Thanking in advance. EDIT: Function takes something and if function is defined as a set that it should behave in the same way but set does not behave in that way.
What is meant by a function on a set. - Mathematics Stack Exchange
2022年7月21日 · For a decent description of what a function really is, consider looking at Halmos's Naive Set Theory. When I say "what it really is", I mean "a set theoretic object that has all the properties that we want a function to have, so that we can use it …
real analysis - Proving set function is countably additive ...
2024年10月4日 · How to show discrete measure $\mu$ is an additive set function? 2 If a set function on a semiring is finitely additive and continuous at the empty set, then is it necessarily a premeasure (i.e., countably additive)?
Is a function a set or a rule? - Mathematics Stack Exchange
2024年1月21日 · The idea there would be to approximate either the logarithm function, or one of the trigonometric functions, by the function whose rule is given by looking up the nearest values in a large set of samples to the input, and then performing linear interpolation between the two nearest samples.
Problems with Set Function - Mathematics Stack Exchange
2020年8月8日 · The finite additivity on my set function doesn't give this, hence either my calculations are wrong or my set function is not finitely additive. Which is true? What should be $\mu^{*}(c,\mathbb{Q})$ and $\mu^{*}(c,\ln(\mathbb{Q}_{>0}))$ instead? Edit: According to a recent answer, the set function is not well-defined for this specific case. Here ...
What is a set of functions? - Mathematics Stack Exchange
How to tell if relation on set is a partial order when relation is defined as a set of ordered pairs? 3 One to One Correspondence between the Set of All functions
Proving a set is a function - Mathematics Stack Exchange
2019年8月27日 · Well, that function takes pairs of real numbers $(x,y)$ into $(3y,2x,x+y)$. Thus, the domain of that function, $\theta$ , is $\mathbb R^2$ and the codomain is $\mathbb R^3$ .