I came across a paper, where the notation is:

where is a set,

Normally we see exponential such as , where n is a real number.

How should I interpret 2^Theta, is this a matrix where in each entry the base is 2?

Thanks for help.

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- May 1st 2012, 06:54 AMcolruytHow to understand set as exponential?
I came across a paper, where the notation is:

where is a set,

Normally we see exponential such as , where n is a real number.

How should I interpret 2^Theta, is this a matrix where in each entry the base is 2?

Thanks for help. - May 1st 2012, 07:06 AMModusPonensRe: How to understand set as exponential?
It's the set of all functions from theta to {0,1}.

- May 1st 2012, 07:06 AMPlatoRe: How to understand set as exponential?
- May 1st 2012, 07:22 AMcolruytRe: How to understand set as exponential?
Thanks a lot.

I don't understhand the first meaning:Quote:

It stands for the set of all functions from A to {0,1}

Actually I think it might be the case for power set, since this comes with a definition for a function:

- May 1st 2012, 07:31 AMPlatoRe: How to understand set as exponential?
- May 1st 2012, 07:36 AMHallsofIvyRe: How to understand set as exponential?
No, he means that 2^A is a

**set**of functions- the set of all functions from A to {0, 1}. And it is to {0, 1} because of the "2". 3^A would be a**set**of all functions from A to {0, 1, 2}, or more generally, from A to any set containing 3 objects.

Quote:

Actually I think it might be the case for power set, since this comes with a definition for a function:

- May 1st 2012, 07:37 AMcolruytRe: How to understand set as exponential?
Sorry my mistake: basically it's a function that matches two sets into two sets, think of match students into schools. where is the preference of students, and a typo in my previous function, the correct form is:

My original guess was power set too, but I am just no sure about the notation...