how to prove that the set "all f with f(0) = f(1)", function has domain containing 0 and 1; is a linear space?

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- Aug 28th 2012, 07:25 AMakash1600problem on determining if a set is a linear space
how to prove that the set "all f with f(0) = f(1)", function has domain containing 0 and 1; is a linear space?

- Aug 28th 2012, 07:33 AMPlatoRe: problem on determining if a set is a linear space
Do you know what a linear space is?

- Aug 28th 2012, 09:56 AMHallsofIvyRe: problem on determining if a set is a linear space
The standard way of proving "X is Y" is to use the definition of X to show that it also satisfies the definition of Y.

Here, X is the all functions, f, such that f(0)= f(1). Now, you need to show that that set satisfies the definition of "linear space"- that's just what Plato is asking.