[butlike]

OK this one still trips me up. Why isn't 5/0 5? If I have 5 apples, and I divide that group by 0, I STILL HAVE 5 APPLES. If I have 5 apples, and I divide that group by 2, I have 2 groups of 2.5 apples.

[t0mpr1c3]

Because 0 is not 1.

Consider the equation x = 5/y. Let us assume that the variable x is defined for every value of y. Then x * y = 5 (after multiplying both sides by y).

Let us also assume, as you suggest, that when y = 0, x = 5/0 = 5.

Then x = 5 = x * y. The only solution to this equation is y = 1, a contradiction.