Quote Originally Posted by Duke_of_URL View Post
SNIP... He would even do a divide by zero, whence it would flash 8's or E's. He went on to explain asymptotic behavior to us 6th graders by asking us what 12 divided by 12 was, then divided by 6, then 4, and 3, 2, 1. He then asked us if we noticed the answers were getting larger and larger? Next he asked what it would be when we divided by zero, which he did, saying it was so large that it is, "infinite." Wow, I'd just gotten a math lesson that made sense! I look back on that event fondly, even though the persons' names have escaped me. As for me, I'd go on to earn my BS and MS in Engineering with a strong emphasis in Electronics and Mathematics. Perhaps that friend's dad that day had lit a fire?
Another way to explain division by zero is to view division as the process of counting how often one can subtract the divisor from the dividend before reaching zero.

An example dividing dividend 6 by divisor 2.

start quotient = 0
6 - 2 = 4 quotient = 1
4 - 2 = 2 quotient = 2
2 - 2 = 0 quotient = 3

now do the same thing with a divisor of zero

start quotient = 0
6 - 0 = 6 quotient = 1
6 - 0 = 6 quotient = 2
6 - 0 = 6 quotient = 3
...

As one can see, the quotient will keep growing forever (in math terms, becomes infinite) while the dividend remains unchanged.