I Proof: 0.9999 does not equal 1

  • Thread starter Math401
  • Start date
Or rather counter proof.
They said x=0.999...
10x=9.999....
9x=9.999....-x
9x=9
x=1
but this is obviously wrong, you can't substract infinity from infinity unless you consider infinity a number and if so then you would get 8.99...1 and not 9. either way 0.999....= 1 is wrong. and is not different than saying (0.999...) +x=1.99...8 you can't add an infine amount of nines to an infinite amount of nines or subtract. if you could then you would consider infinity as a number and in that case the proof is also wrong
 

DrClaude

Mentor
6,687
2,816
This subject has been discussed many times on PhysicsForums. Please do a search of the forum or look at the "Similar Discussions" links below.

Yes, 0.999... = 1.

0.999... = 1 because, by the definition of "decimal place notation", 0.999... is the limit of the infinite series .9+ .09+ .009+ .... That's a geometric series and it's easy to show that the limit is 1.
Thread closed.
 
32,167
4,033
but this is obviously wrong, you can't substract infinity from infinity
We are not subtracting infinity from infinity here. The subtraction is 9.999... - 0.999..., with each number having an infinte number of 9 digits to the right of the decimal point. The result is 9.000..., with an infinite number of 0 digits to the right of the decimal point.
As DrClaude said, this has been discussed many times here at PF.
 

Want to reply to this thread?

"Proof: 0.9999 does not equal 1" You must log in or register to reply here.

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving

Top Threads

Top