Another argument that may be more convincing on a gut level:
9x(1/9) is exactly equal to 1, correct?
Find the decimal representation of 1⁄9 using long division:
1/9=0.11111111… (note there is no different or superior way to represent this number as a decimal)
9x(1/9) = 9x(0.11111111...)=0.9999999… which we already agreed was exactly equal to 1.
Another argument that may be more convincing on a gut level:
9x(1/9) is exactly equal to 1, correct?
Find the decimal representation of 1⁄9 using long division: 1/9=0.11111111… (note there is no different or superior way to represent this number as a decimal)
9x(1/9) = 9x(0.11111111...)=0.9999999… which we already agreed was exactly equal to 1.
Yes :)
See my previous (edited) comment above.
Oh sorry, my bad. I should have read the thread. Or the link.
No problem. It is a great proof (there aren’t many so simple and succinct). Just bad luck on timing ;)