Symmetry of two boson particles From what I understand from the textbook, a two-particle bosonic wave function is symmetric, because you can exchange the position of the two particles and have the same wave function. But I think exchanging the position has nothing to do with symmetry. Symmetry means $f(x)=f(-x)$, not exchanging position. So I am confused. What does symmetry mean in this context?
 A: We the physicists use to speak in a very particular way, but we don't notice because we are used to it. Lazyness makes us ommit many surnames, but all symmetries need a surname. You can't say "a function is symmetrical", you should say "a function is symmetrical to the y-axis. You always have to specify the reference, at least once (before it is assumed). 
Okay, so... In this context (and in general when we talk about functions of many variables...)

A function is said to be symmetrical under permutation of two of its variables if the exchange of them leaves the function invariant.

Mathematically, given a function (of many variables, otherweise it'd be nonsense) 
$$f(x_1,x_2,\dots)$$
The function is symmetrical under permutation of $x_1$ and $x_2$ if
$$f(x_1, x_2, \dots ) = f(x_2, x_1, \dots )$$
By the way, it's said to be "antisimetrical" if $f(x_1, x_2, \dots ) = -f(x_2, x_1, \dots )$
A: Because bosons are not fermions they do not obey Pauli exclusion principle. Hence they can have same quantum states. Thus if you stack up 2 bosons you should expect that the wave functions should not be different otherwise they aren’t bosons. Hence this symmetry. If symmetry would not exist then these would be fermions because of Pauli’s exclusion principle. 
