# Python, 13

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If the OP wants all functions to be non-anonymous, add `f=` to the front of each for two additional characters.

    lambda x:x//1

Since `x%1` returns the amount following the decimal point, this is pretty short (14):

    lambda x:x-x%1

If using cast to integer instead, it's one character longer (15):

    lambda x:int(x)

The shortest using string casting I could come up with (40):

    lambda x:int(`x`.split('.')[0])+cmp(x,0)