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Does 0.9999(repeating) = 1?

Yes 705 56.9%
No 578 46.65%
Voters 1239 .

Does 0.9999(repeating) = 1?

Eledhan

Senior Member

Quote:
Colonel J:
612 people, and counting, are retarded.

I just made it 613...pretty simple once you understand that the only reason you ever saw a number with repeating decimals was an attempt to represent the same concept in a different system.

Kodoku

Senior Member

Quote:
If you can't say that there is a difference between x and y if they are the same, then why bother with representing .999~ and 1.000~ at all if they are the same number? It seems to be an exercise in futility.
Because in math, we tend to define things generally. We didn't define decimal expansions number by number, we defined the decimal expansion in general. As it so happens, there is a decimal expansion for every single number, and because of repeating 9s (or repeating 1s in base 2, or in general, repeating n in base (n+1)), many numbers have two decimal expansions. It's similarly to how you can represent the same number as many different quotients. 1/1 = 2/2 = 3/3 = 4/4 etc.
Quote:
Yes, both numbers represent one whole "numerical unit". In essence, if it were a pie, you could say you have a whole pie (1/1 or 1.000~), or three thirds of a pie (3/3 or .999~). They all mean the same thing... Is this the point of the whole topic?
Well the point is whether or not this is in fact the case, but yes, those would all mean the same thing though it would be very odd to express an intact pie as anything other than "one pie".

Turbo Sawka

Senior Member

0,(9) = 1

because math.
in my country its like 12 year old level of education. dumb**** americans.

hahahahahah 70 pages of discussion on something so obvious.
only in retardcountry. a failure in the eyes of whole world. fats and idiots cummulated on 9mln sq meters.

IS14696195e1336cdef530a

Senior Member

My question is
1+1=2
0.99...+0.99.... is that equal 2 then ??
or equal 1.99........ and then theoretically end with an 8, even though its endless and dont end :P ?

also is the number 999.... =100..... ?

Eledhan

Senior Member

Quote:
Kodoku:
Because in math, we tend to define things generally. We didn't define decimal expansions number by number, we defined the decimal expansion in general. As it so happens, there is a decimal expansion for every single number, and because of repeating 9s (or repeating 1s in base 2, or in general, repeating n in base (n+1)), many numbers have two decimal expansions. It's similarly to how you can represent the same number as many different quotients. 1/1 = 2/2 = 3/3 = 4/4 etc. Well the point is whether or not this is in fact the case, but yes, those would all mean the same thing though it would be very odd to express an intact pie as anything other than "one pie".

Well, of course that would be odd...hence the trouble most people (myself included...and I have a bachelor's degree in Accounting...where I had to take calculus, advanced statistics, etc.) have when it comes to these kinds of things. Part of my problem was not remembering the principle being taught and only coming across it in things like accounting work where you NEVER EVER use the actual decimal if the decimal requires more than 2 decimal places to represent dollar amounts. Sure, we use extended decimals beyond the hundredths place for things like percentages and ratios, but those are always rounded at some point as well, since they are almost always applied to a dollar figure at some point along the way.

Kaolla

Senior Member

Quote:
Eledhan:
However, the representation .111~ is the closest possible representation to the value of 1/9

*in our currently accepted decimal form.

1/9 = .111 R1/9 in my handy extended notation

9 x 1/9 = 9 x .111 R1/9 = .999 R9/9 = 1

ain't it a thing of beauty? no approximation, just clean EXACT math

Crowcide

Senior Member

Quote:
Kodoku:
many numbers have two decimal expansions.

Every number has a unique infinite decimal expansion, well known theorem of the reals.

Eledhan

Senior Member

Quote:
Turbo Sawka:
0,(9) = 1

because math.
in my country its like 12 year old level of education. dumb**** americans.

hahahahahah 70 pages of discussion on something so obvious.
only in retardcountry. a failure in the eyes of whole world. fats and idiots cummulated on 9mln sq meters.

I notice you failed to mention which country you live in...I wonder why? I have a hunch it's because the wealthiest people there are equivalent to near poverty levels here...hmmmm....

And besides, I just found out that this entire concept is taught to middle school students here in the USA (12-15 year olds). I'm 27 (today, actually), and I have not used this kind of math in years...so I didn't remember all the nuances of it. That doesn't make me retarded. I happen to know quite a bit of high-level math/science/philosophy. Ignorance of one aspect in a specific field does not equate to retardation.

Or did you not learn that problem solving skills are better than rote memorization in school?

/rant

Kaolla

Senior Member

Quote:
Turbo Sawka:
0,(9) = 1

because math.
in my country its like 12 year old level of education. dumb**** americans.

hahahahahah 70 pages of discussion on something so obvious.
only in retardcountry. a failure in the eyes of whole world. fats and idiots cummulated on 9mln sq meters.

wow, someone is angry that he doesn't live here. soooo jealous

Crowcide

Senior Member

Quote:
Kaolla:
*in our currently accepted decimal form.

1/9 = .111 R1/9 in my handy extended notation

9 x 1/9 = 9 x .111 R1/9 = .999 R9/9 = 1

ain't it a thing of beauty? no approximation, just clean EXACT math

All of the arguments about decimal fraction representation or setting x = .999~ are essentially circular arguments. .999~ = 1 cause of definition no other reason.