Yes, a function basically corresponds to a rule which says "you give me a value, and I'll give you a single value back in return". You don't even need an explicit formula for a function.

If I say "give me 3 and I give you the value 1 back; give me 5 and I give you the value 4 back" then that is a perfectly good function defined on the set of elements 3 and 5.

What you can't do is say "give me the number 4 and sometimes I'll give you back the number 2 and other times I'll give you back the number 7" - that isn't a function!

Reply 7

Namige

17

Original post by davros

Yes, a function basically corresponds to a rule which says "you give me a value, and I'll give you a single value back in return". You don't even need an explicit formula for a function.

If I say "give me 3 and I give you the value 1 back; give me 5 and I give you the value 4 back" then that is a perfectly good function defined on the set of elements 3 and 5.

What you can't do is say "give me the number 4 and sometimes I'll give you back the number 2 and other times I'll give you back the number 7" - that isn't a function!

Yes it is if you have a probability function.

Reply 8

yo radical one

6

Imagine if it was one-many

how would you decide what the output of any given input is?

Reply 9

davros

16

Original post by Namige

Yes it is if you have a probability function.

All right!

I should have said "you can't have a rule that gives you back more than one value simultaneously" :smile:

Reply 10

james22

16

Original post by Namige

Yes it is if you have a probability function.

They aren't functions in the classical sense. Any mapping which can send an element of the domain to more than 1 element of the codomain is not a function by definition.

Reply 11

Namige

17

Original post by davros

All right!

I should have said "you can't have a rule that gives you back more than one value simultaneously" :smile:

That's called a many to one function.

Reply 12

davros

16

Original post by Namige

That's called a many to one function.

No that's called "one to many" (or sometimes multivalued)

"Many to one" is when multiple inputs can be mapped to the same output e.g. sin x = 0 for x=0, pi, 2pi etc. "Many to one" is perfectly acceptable within anyone's definition of a function.

By the way, what sort of thing did you have in mind when you referred to a "probability function"?

Reply 13

Namige

17

Original post by davros

No that's called "one to many" (or sometimes multivalued)

"Many to one" is when multiple inputs can be mapped to the same output e.g. sin x = 0 for x=0, pi, 2pi etc. "Many to one" is perfectly acceptable within anyone's definition of a function.

By the way, what sort of thing did you have in mind when you referred to a "probability function"?

One that gives random values for an input. For example 7 could give 6 and at other times give pi.

Reply 14

davros

16

Original post by Namige

One that gives random values for an input. For example 7 could give 6 and at other times give pi.

That's what I thought you probably meant.

Do you deal with these things on a practical basis? How might you construct a function that behaves in that way?

I was just wondering whether there is any such thing as a truly "probabilistic" function, or whether it is just a function of several (possibly hidden) variables - e.g. your number 7 as well as another input (not controlled by you) such as the number of seconds since Jan 1 1970.

(Not my area of expertise - hence why I'm asking the question!)