If x/y means distributing x into y groups and measuring the size of a group, then x/0 means distributing x into zero groups, in other words doing nothing, so the answer could be zero. If x/y means counting how many times you can subtract y from x, the answer is infinity. Edit: also, if 50/0 = infinity, infinity * 0 = 50 ... or any other number.
(_Felix's school of dance and occult sciences,
Thu 31 Jan 2008, 16:49,
archived)
Division (horticulture): a method of vegetative plant propagation, or the plants created by using this method
(pzykoQuery failed.,
Thu 31 Jan 2008, 16:52,
archived)
your first case
would result in "undefined". doing nothing isn't the same as having a well-defined answer of zero.
edit: and since infinity isn't actually a number your second point is not true