Why does 1/0 make infinity?

If 1 divided by 0 makes infinity, it means infinity times 0 is one. But zero doesn't add up to anything. Or does it?

Divide 1 by 3, using long multiplication. It will come to 1/3, or 0.333333333333333.....
note that the line of threes is infinite.

Now multiply this by 3.
1/3 times 3 equals....
1

0.333333333333333........... times 3 equals...
0.999999999999999............

But wait! It should be 1 ! Why?
Because 1/3 and 0.33333... are equal. Times three, they both should equal one.
So that means 0.999999..... is actually 1 !

Now back to the first part. Why does infinity times 0 = 1?
This is because 1-0.999999999999999999999.... = 0
(remember, 0.999999999...... is 1.)
But 1-0.99999....= 0.000......1
This means that 0 and 0.000000......1 are the same.

So if you multiply that tiny 0.000000....1 by infinity, by the power of infinity, it will be 1.













































Hi. James Dai