a concept of infinity that I always thought of on this subject (ever since questioning the math teacher, and him being unable to tell me much of infinite geometric sequences [

]) was that Infinite is any number than cannot really have an end value pasted on it... something like a destination, rather than a number. just like the horizon, you know it's there, but you will never reach it.

say, perhaps, you have point a, and point b. point a is 25 centimeters from point b. but it can also be measured in inches, half inches, millimeters, feet, tens of feet, in infinite number of ways, because the list never ends.

but then you have the size of infinity.

the 1+2+3+4 example is one way, but I thought of another definite way to put it. 1/0 is infinite, because of the process used in division. in division, you essentially subtract the denominator from the numerator, increase the end result by 1, and then repeat until you cannot subtract anymore.

for 8/2, it would go like this:

8-2 = 6, result = 1

6-2 = 4, result = 2

4-2 = 2, result = 3

2-2 = 0, result = 4. can no longer subtract, therefore 8/2 = 4.

but for 1/0, it would go like this:

1-0 = 1, end result = 1

1-0 = 1, end result = 2

1-0 = 1, end result = 3

...

that cycle will never end, so therefore, the end result is infinite.

but say you turn it into 2/0, it would be a infinite that is larger, since, if you could put it another way, and you divide them, (2/0)/(1/0), then you divide the denominators, assign that as a value of 1, because any identical values divided will equal one, then the numerator becomes 2. Therefore, theoretically, 2/0 as an infinity is twice as large as 1/0.

however, you can also say that 0/0 is an infinite, invalidating the previous paragraph.

but given the fact that I don't really yet know calculus, and haven't worked with infinity much, I don't know if my thoughts are really valid.

anybody care to correct me?