This is a fairly old topic so I'm not sure if all of you have heard about this. I just found out about it and found it interesting.
The claim is that 0.9999.....(infinite 9s) is equal to 1.
Here are some proofs
|x = 0.9999…||given|
|10x = 9.9999….||multiply by 10|
|9x = 9||subtract x|
|x = 1||divide by 9|
|0.999... = 1||substitution|
What's the difference between 1 and 0.9999....? Their difference is 0.0000....The zeroes will stretch out infinitely and we will never reach 1. Therefore, 0.00000...can be simplified to 0.
If the difference between any two numbers is 0, then they are of the same value.
On the number line, there is no real number between 0.99999..... and 1. If there is no real number between any two numbers, then those two numbers are of the same value. There is no number higher than 0.9999... and lower than 1, therefore they are of the same value.
1= 5/7 + 2/7
1= 0.714285714285.... + 0.285714285714......
Sum of an infinite convergent geometric series
and many more