A Craps Tutorial

Other Topics Section    --    Bracket Function Properties

	Theorem   1
		If x is any real number and t is any integer then
			x + t   =     x   +   t

Theorem 1 is obviously true if x and t are both integers.
So, let's assume that x is not an integer.

Then x must lie between two consecutive integers,   say   k and k+1 :
         k   <   x   <   k+1

Obviously   k = x .

Adding t throughout the above inequality   we get
k + t   <   x + t   <   k+ t + 1

Note that x + t lies between the consecutive integers   k+t   and   k+t+1

Therefore,   x + t   =   k + t   =   x   +   t