.999999999999...=1

First of all yes, please forgive my European notation ;-)

Quote from: Ozymandiax on August 10, 2011, 02:56:43 PM

There are infinite real numbers between 0 and 1, this lead us to the fact that for any iota ( ANY ) that allows me to consider:
x+i = 1, even if x= 0,99999999999999999.. ( you put as many 9's here as you want ), "i" is still NOT 0

The fact that there are infinite 9s cancels out the fact that there are infinite numbers between 0 and 1.  Would you dispute the fact that 0,333... is equal to 1/3?  If you do, I wish you luck in the third grade; if not, I hope you realize that it is the same principle at work here.  Technically you can put as many 3s after the decimal point you want, it will still not be equal to 1/3 (which by definition can't be expressed by a terminating decimal anyway); but if it's understood that there are an infinite number of 3s after the decimal point, it is equal to 1/3.

0,333... x 3 = 0,999...; do you dispute the logic?

1/3 x 3 = 1; do you dispute the math?

Therefore, 0,999... = 1.

In other words, there is no iota.

About the topic; I am not discussing the logic nor the math. However..... (1/3) X 3 = 1  ... Absolutely OK, nothing to say..

0,3333 X 3 = 0,9999 .... how many 3?

Maybe this is just spinning out; what I say is that THERE is, a difference, a Iota, between these infinite "3", or "9", and the complete number. It is just out of convenience, and because it is much better, that we type 1/3 instead of the zillions of 3`s ... and this is precisely the point... 1/3 is a solid complete number; so it is 1.

I understand your point ( for real), but I only can accept that 0,999999 (period) IS 1 as APROXIMATION.

Again, for most common uses, even Pi can be considered as 3,1416 ... but it is NOT. Pi is Pi ..... and NO short description of Pi ( even with zillions of numbers) is Pi

1) (1/3) + (1/3) + (1/3) = 1

2 ) The 0,3333 version.......... I cannot support it from an strict mathematical point of view. Again, I can accept it as approximation.

I'd use a pregnancy simile.. but unsure if it's out of rules :-P

First of all yes, please forgive my European notation ;-)

Quote from: Roundy the Truthinessist on August 10, 2011, 07:38:15 PM

Quote from: Ozymandiax on August 10, 2011, 02:56:43 PM

There are infinite real numbers between 0 and 1, this lead us to the fact that for any iota ( ANY ) that allows me to consider:
x+i = 1, even if x= 0,99999999999999999.. ( you put as many 9's here as you want ), "i" is still NOT 0

The fact that there are infinite 9s cancels out the fact that there are infinite numbers between 0 and 1.  Would you dispute the fact that 0,333... is equal to 1/3?  If you do, I wish you luck in the third grade; if not, I hope you realize that it is the same principle at work here.  Technically you can put as many 3s after the decimal point you want, it will still not be equal to 1/3 (which by definition can't be expressed by a terminating decimal anyway); but if it's understood that there are an infinite number of 3s after the decimal point, it is equal to 1/3.

0,333... x 3 = 0,999...; do you dispute the logic?

1/3 x 3 = 1; do you dispute the math?

Therefore, 0,999... = 1.

In other words, there is no iota.

About the topic; I am not discussing the logic nor the math. However..... (1/3) X 3 = 1  ... Absolutely OK, nothing to say..

0,3333 X 3 = 0,9999 .... how many 3?

Maybe this is just spinning out; what I say is that THERE is, a difference, a Iota, between these infinite "3", or "9", and the complete number. It is just out of convenience, and because it is much better, that we type 1/3 instead of the zillions of 3`s ... and this is precisely the point... 1/3 is a solid complete number; so it is 1.

I understand your point ( for real), but I only can accept that 0,999999 (period) IS 1 as APROXIMATION.

Again, for most common uses, even Pi can be considered as 3,1416 ... but it is NOT. Pi is Pi ..... and NO short description of Pi ( even with zillions of numbers) is Pi

1) (1/3) + (1/3) + (1/3) = 1

2 ) The 0,3333 version.......... I cannot support it from an strict mathematical point of view. Again, I can accept it as approximation.

I'd use a pregnancy simile.. but unsure if it's out of rules :-P

Good luck in the third grade.

You obviously don't grasp the concept of infinity.

About the topic; I am not discussing the logic nor the math. However..... (1/3) X 3 = 1  ... Absolutely OK, nothing to say..

0,3333 X 3 = 0,9999 .... how many 3?

Maybe this is just spinning out; what I say is that THERE is, a difference, a Iota, between these infinite "3", or "9", and the complete number. It is just out of convenience, and because it is much better, that we type 1/3 instead of the zillions of 3`s ... and this is precisely the point... 1/3 is a solid complete number; so it is 1.

So what is this number that comes after infinity?

Infinity and a half, duh.

I thought it was infinity + 1 :-D

I will revise my 4th grade concepts :-D

Anyway, since I am going to have vacation tomorrow I will take calculus again ;-)

OK, anyone can rectify and some1 said it is wise to do so.

After some mathematical research ( beyond 3rd grade ;-) I must change my opinion and recognize that after all 0.999999999999..... is as well a valid representation of 1

Please, accept my apologies for all previous messages since I understand that I should have made this research before posting.

have a good day.

OK, anyone can rectify and some1 said it is wise to do so.

After some mathematical research ( beyond 3rd grade ;-) I must change my opinion and recognize that after all 0.999999999999..... is as well a valid representation of 1

Please, accept my apologies for all previous messages since I understand that I should have made this research before posting.

have a good day.

You mean, you looked this up on google?

Quote from: Ozymandiax on August 12, 2011, 03:02:55 AM

OK, anyone can rectify and some1 said it is wise to do so.

After some mathematical research ( beyond 3rd grade ;-) I must change my opinion and recognize that after all 0.999999999999..... is as well a valid representation of 1

Please, accept my apologies for all previous messages since I understand that I should have made this research before posting.

have a good day.

You mean, you looked this up on google?

Can the internet not be used for valid research?

Quote from: Ozymandiax on August 12, 2011, 03:02:55 AM

OK, anyone can rectify and some1 said it is wise to do so.

After some mathematical research ( beyond 3rd grade ;-) I must change my opinion and recognize that after all 0.999999999999..... is as well a valid representation of 1

Please, accept my apologies for all previous messages since I understand that I should have made this research before posting.

have a good day.

You mean, you looked this up on google?

No, I mean that I consulted some mathematician friends, and that I revised some Math books, and therefore I changed my mind

:-)

Quote from: Mr Pseudonym on August 12, 2011, 05:48:45 AM

Quote from: Ozymandiax on August 12, 2011, 03:02:55 AM

OK, anyone can rectify and some1 said it is wise to do so.

After some mathematical research ( beyond 3rd grade ;-) I must change my opinion and recognize that after all 0.999999999999..... is as well a valid representation of 1

Please, accept my apologies for all previous messages since I understand that I should have made this research before posting.

have a good day.

You mean, you looked this up on google?

Can the internet not be used for valid research?

Of course it can.  However, mathematical research sounds like he is trying a lot harder than just putting 0.999 into a google search and going to the first answer on the search page result.  That so happens to be the Wiki page that says this about the situation;

"In mathematics, the repeating decimal 0.999... (which may also be written as 0.9, , 0.(9), or as 0. followed by any number of 9s in the repeating decimal) denotes a real number that can be shown to be the number one. In other words, the symbols 0.999... and 1 represent the same number"

That took me all of about 5 seconds to find.  It explains it all and even includes this little number (pardon the pun);
With the rise of the Internet, debates about 0.999... have escaped the classroom and are commonplace on newsgroups and message boards, including many that nominally have little to do with mathematics.

Also from the same wiki page;


Q: How many mathematicians does it take to screw in a lightbulb?
 

A: 0.999999....

It's not all of Europe, but several countries do do it. That's the way I've been taught, and I had to go through a painful switching process when I moved to the UK.
Basically, those countries use a comma as a decimal point and a dot as a separator in large numbers.
0,5 would be 1/2, whereas 1.000.000 would be one million.

Sorry to back to sort of off topic, but are saying that in the we write 1 million as 1.000.000 and 1/2 as 0,5 ?

We don't. Then again I may have misread your post and you infact meant that other coutries do the above but that the UK do not.