What is the meaning of ‘!’ In math and how do I use it?

In math, the '!' sign are used in factorial. Factorial is multiplications on numbers itself and with another numbers that less than the number itself. Example :

5! =5x4x3x2x1 or nx(n-1)x(n-2)...2x1

if he is naked in public on purpose then yes. that is a crime and you should call the police as he could be a threat to females/ might flash.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.