I know there are proofs on this but I’m not great at math, can someone dumb it down for me?
In: Mathematics
The very simple answer is there’s no “room” between 0.999… and 1 for another number.
The three dots (…) is called an ellipsis and it means “keep doing that forever” in maths. And for 0.999… it means “keep writing nines forever”.
But let’s see if we can find any room between 0.999… and 1. The easiest way would be to subtract 0.999… from 1. What does that equal? You’ll have to “carry the 1” and turn 1.0 in to 0.¹0 repeatedly.
1.000 – 0.999… = 0.¹000 – 0.999… = 0.100 – 0.099… = 0.0¹00 – 0.099… = 0.010 – 0.009…, etc, which might end up with 0.000…1 .
But what would “0.000…1” mean? “Zero point zeroes forever and then one” doesn’t make much sense.
**Alternate approach from the other direction**
What does 0.999…. mean?
* 0.9 = 9/10, is nine tenths (leaves one tenth of “room”)
* 0.99 = 99/100 is ninety hundredths (leaves one hundredth of “room”)
* 0.999 = 999/1000 is nine hundred and ninety nine thousandths (leaves one thousandths of “room”)
* 0.9999999 = 9,999,999/10,000,000 is nine million, nine hundred and ninety-nine thousand, nine hundred and ninety-nine out of ten million (leaving one ten-millionth of “room”)
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