Wikipedia tends to be an excellent resource for math and computer science concerns. Care should be taken when using it as a resource for information regarding a current situation, or a situation in which there are disputing narratives.veloper said:
Poll: Does 0.999.. equal 1 ?
- Thread starter mattsipple4000
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1/3 = 0.3 recurringAphex Demon said:
0.3 recurring X 3 = 0.9 recurring and 3/3
3/3 = 1
Answer: YEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEES.
Why must you people keep asking?!
From Wikipedia on the subject (and my Dad is a Maths teacher, so I know this paragraph is right anyway):
"The equality 0.999... = 1 has long been accepted by mathematicians and taught in textbooks to students. In the last few decades, researchers of mathematics education have studied the reception of this equality among students, many of whom initially question or reject it. Many are persuaded by an appeal to authority from textbooks and teachers, or by arithmetic reasoning as below to accept that the two are equal. However, some are often uneasy enough that they seek further justification."
The only reason people have trouble with it is that you can't easily work with infinity using real numbers.
All of the extra 9's adding to the end means that it tends towards 1, which means that by the time you've gone through an infinite number of iterations, you have 1.
Obviously, we can't do that, so people are just falling back on 'I can't see it so it's wrong'.
All of the extra 9's adding to the end means that it tends towards 1, which means that by the time you've gone through an infinite number of iterations, you have 1.
Obviously, we can't do that, so people are just falling back on 'I can't see it so it's wrong'.
If you have any doubt about a Wikipedia's math article, your only better source will be a direct conversation with an expert in the field. I mean, even bypassing books, because books can also be erroneous (especially on middle school-type stuff, such as the OP question). A thousand forums are not nearly as good as 1 Wikipedia math article. I have no idea why it happens to be this way, but I can tell you that I have a masters degree already, am a doctoral candidate, and still Wikipedia's math articles are an everyday reference for me. (Even if I can't cite them in a paper). Everything else on Wikipedia (except maybe sports statistics) is not remotely as well-written, detailed, or correct.mattsipple4000 said:thanks! you can never count on it to be 100% correct tho
I said yes. 0.999... is close enough to 1 that it should be allowed the same kind of priviliges and respect. Just because human logic is slightly flawed in this area because our minds cant comprehend infinity doesn't mean that we should discriminate agaisnt 0.999... that would be just unfair. And to all of you who say 0.999... does NOT equal one, your a bunch of capitalist scum sucking pigs! ALL NUMBERS ARE EQUAL!
.....Except for 0. I mean, where does that asshole get off...
.....Except for 0. I mean, where does that asshole get off...
0.9999... = 1 Yes
but it does NOT = 1.0000...
1 is a number with a defined decimal places, meaning that it could be anything from 0.5000... to 1.4000... (probably even tighter gaps there but whatever)but it no longer equal those numbers if you add a decimal point...
but it does NOT = 1.0000...
1 is a number with a defined decimal places, meaning that it could be anything from 0.5000... to 1.4000... (probably even tighter gaps there but whatever)but it no longer equal those numbers if you add a decimal point...
There is no rounding going on. As I explained in my previous post:kebab4you said:
Basically if you were rounding, you would be adding a small bit to the 0.999.. to make it fully equal to 1 right? Well that small bit you want to add doesn't exist. Any real number you could possible imagine added to 0.999... would make it a HIGHER number than 1.
0.0...01 doesn't exist. You can never reach the 1 on the end. That digit can and will never come up, and doesn't exist.
Wrong, as per above.Nile McMorrow said:
Though my this rationality, every number conceived is the same as every other number, when looked at through the focus of infinity.
.(9)=1 because doing so in any other way forces you to invent new objects or numbering systems.
It's just a quirk in expression, a solution made in convention that makes other solutions work out, not some grand philosophical expression.
.(9)=1 because doing so in any other way forces you to invent new objects or numbering systems.
It's just a quirk in expression, a solution made in convention that makes other solutions work out, not some grand philosophical expression.
Why do people never accept the most trivial proof?
1 - 0.(9) = 0.(0)1.
Define 0.(0)1 = 0 (as we are working in an Archimedean numbering system).
QED.
People don't seem to understand that it is possible to describe a system where the two aren't equal. It's just more consistent to define infinitesimals as zero than for e.g. 9/9 to be different than 1.
1 - 0.(9) = 0.(0)1.
Define 0.(0)1 = 0 (as we are working in an Archimedean numbering system).
QED.
People don't seem to understand that it is possible to describe a system where the two aren't equal. It's just more consistent to define infinitesimals as zero than for e.g. 9/9 to be different than 1.
No, of course 0.(9) doesn't equal 1. It goes 0.999... to infinity.
Now granted, if you use the value of 0.(9) in real-life applications, you might indeed decide that the approximation error from 0.(9) to 1 is neglijible and just consider it 1.
But from a purely mathematical point of view, no, 0.(9) does NOT equal 1.
EDIT :
Same issue for something that is infinitely small like 0.000000...00001 . Is it equal to zero? No, of course not, it represents a very,very small but non-zero value.
In actual applications would you care that 0.0000....001 is not zero ? Most of the time,no. But it depends on the scale of magnitude of applications.
It all comes down to approximations and how they are relevant to a context.
Now granted, if you use the value of 0.(9) in real-life applications, you might indeed decide that the approximation error from 0.(9) to 1 is neglijible and just consider it 1.
But from a purely mathematical point of view, no, 0.(9) does NOT equal 1.
EDIT :
Same issue for something that is infinitely small like 0.000000...00001 . Is it equal to zero? No, of course not, it represents a very,very small but non-zero value.
In actual applications would you care that 0.0000....001 is not zero ? Most of the time,no. But it depends on the scale of magnitude of applications.
It all comes down to approximations and how they are relevant to a context.