Poll: Does 0.99 Recurring = 1

hendrix · 31 Oct 2004 at 18:01

I'm moving onto Proofing soon in maths, so this should be fun asking the teacher

1/3 = 0.3r

2/3 = 0.6r

1/3 + 2/3 = 3/3 = 1

0.3r + 0.6r = 1

Thats what i believe

Jokester · 31 Oct 2004 at 18:01

Originally posted by sid
I am strongly technically minded person/

Can somebody tell me whether 0.9r is excatly 1 only at the limit.

If the number of 9s after the decimal place is stopped b4 infinity then it is surely less than 1. Well after a billion dps it might as well be 1. BUT Thats rounding off and it cant equal EXACTLY 1..

I voted yes btw.

Correct, if it wasn't infinite in length then it wouldn't be 1. By definition though r means that the number is a infinitely repeating decimal.

0.9r = 1

0.49r = 0.5 etc.

Jokester

sid · 31 Oct 2004 at 18:05

Thanks for that jokester

I just realised something that i hadnt realised before

You can express recurring decimal as a fraction

eg 0.1r is same as 1/9

then 0.12r is 12/99

But 0.9r by logic would be 9/9 = 1

Yup its true. I feel convinced by my own logic.

People can choose not to believe that above result. Thats upto them. I think i speak for all people on my side of the debate that when I say that whether or not you believe it has nothing to do with whether it is true or not.

Sid

Glaucus · 31 Oct 2004 at 18:05

Originally posted by Abyss
Here's 2 questions...

Does something that is infintely small exist? If so define it somehow.

Also "if" time is infinite (or going around a circle until you reach the end), is there a beginning or end of time

ok back for one last post then im off this thread

yes cos if its infinite small somthing exists albeit minuscle. other wise it wouldnt be infintely small it would be nothingness.

if you say time has been around for ever then it has no begining and no end and it doesnt form a loop. Thats how i c it but it depends what time therory you want to go by it can be loops donughts weired shapes and therorys.

VDO · 31 Oct 2004 at 18:14

Originally posted by AcidHell2
yes cos if its infinite small somthing exists albeit minuscle. other wise it wouldnt be infintely small it would be nothingness.

Mathematically speaking, something infinitely small would be 0.0r1 (as memphisto would say

), and since there is no such thing, it would equal zero.

Right then, fun as this has been, it's 11:15 PM here (how long before some clever individual says 10.9r:14.9r, you think?), I have school tomorrow, and no shortage of work to do for it. So I shall be off for now, see if this is still running when I return!

Abyss · 31 Oct 2004 at 18:19

Originally posted by AcidHell2
ok back for one last post then im off this thread

yes cos if its infinite small somthing exists albeit minuscle. other wise it wouldnt be infintely small it would be nothingness.

if you say time has been around for ever then it has no begining and no end and it doesnt form a loop. Thats how i c it but it depends what time therory you want to go by it can be loops donughts weired shapes and therorys.

You're saying that there must always be a "miniscule bit" left that means 0.9r is slightly smaller than 1. If this is true, then for something infintely long (e.g. time/circle) there must be that "little bit" left, making it finite in length, thus it must have a start and finish point.

gambitt · 31 Oct 2004 at 18:32

ok next topic:

what is 0^0 (zero to the power of zero)?

have fun

Bakedgoods · 31 Oct 2004 at 18:33

Originally posted by gambitt
ok next topic:

what is 0^0 (zero to the power of zero)?

have fun

Google says 1!

sid · 31 Oct 2004 at 18:33

Originally posted by VDO
Mathematically speaking, something infinitely small would be 0.0r1 (as memphisto would say ), and since there is no such thing, it would equal zero.

I agree

0.0r1 makes no sense

that would be saying that after the decimal point, there are an infinte amount of zeros and then 1 after that. If the number of zeros never ends you cannot put a 1 after that. does anybody understand that??

sid

Duke · 31 Oct 2004 at 18:34

Can this thread get anymore exciting?

p.s 1

gambitt · 31 Oct 2004 at 18:35

Originally posted by sid
I agree

0.0r1 makes no sense

that would be saying that after the decimal point, there are an infinte amount of zeros and then 1 after that. If the number of zeros never ends you cannot put a 1 after that. does anybody understand that??

sid

Well put. That should make perfect sense to the non-maths people.

sid · 31 Oct 2004 at 18:36

Originally posted by Wardie
Google says 1!

3^3/3^3 =3^0 (Basic indicies)

commong knowledge wil tell you that 9/9 is 1

so 3^0 = 1 which also equals 0.9r

0^0/0^0 makes no sense

Dividing by 0 is not defined in maths.

gambitt · 31 Oct 2004 at 18:37

Originally posted by sid
3^3/3^3 =3^0 (Basic indicies)

commong knowledge wil tell you that 9/9 is 1

so 3^0 = 1 which also equals 0.9r

0^0/0^0 makes no sense

Dividing by 0 is not defined in maths.

0^0/0^0 = 1

AlphaNumeric · 31 Oct 2004 at 18:37

Originally posted by Wardie
Google says 1!

The limit as x-> 0 of x^x = 1, but if you do not use a limiting process, it's a much more complex entity.

AlphaNumeric · 31 Oct 2004 at 18:39

Originally posted by gambitt
0^0/0^0 = 1

Thats just making things more complex. After all 0/0 = anything you want depending on the limiting process. 0^0/0^0 = 0^(0-0) = (0/0)^0, which is all "up in the air" unless you consider limits.

Given that most people here don't either understand, beleive or trust limits (since 0.9r is all about limits) you're just inciting another riot I think

sid · 31 Oct 2004 at 18:39

Originally posted by gambitt
0^0/0^0 = 1

If you have no apples

you distribute them between 0 people

does everybody get 1?????

I am open minded about this if proper mathamatical backing is provided.

gambitt · 31 Oct 2004 at 18:40

why not just say, 0^0 = 1 (since it does)

hence 0^0/0^0 = 1/1 = 1

edit: ok, that was a bit of a bold statement, 0^0 should be 1 and there are many arguements for this... I'm going away now before we start all over again!

AlphaNumeric · 31 Oct 2004 at 18:45

Originally posted by gambitt
why not just say, 0^0 = 1 (since it does)

hence 0^0/0^0 = 1/1 = 1

It's a little trickier than that. One way would be to define it as:

Limit(E->0) of:

1 - Int[from E to 1] (Exp(xLog(x))(1+Log(x)))dx

Plug this into a computer and you'll get 0^0 -> 1

sid · 31 Oct 2004 at 18:45

Originally posted by gambitt
why not just say, 0^0 = 1 (since it does)

hence 0^0/0^0 = 1/1 = 1

on my calculator log 0 gives error and

0^0 give error as well

If you raise anything to power 0 you get 1. I no that a standard result ( i explained that myself)

does that include zero as well. ??

sid · 31 Oct 2004 at 18:48

Originally posted by AlphaNumeric
It's a little trickier than that. One way would be to define it as:

Limit(E->0) of:

1 - Int[from E to 1] (Exp(xLog(x))(1+Log(x)))dx

Plug this into a computer and you'll get 0^0 -> 1

Are you like a professor of maths or something

Even for a cambridge maths student, you seem to know helleva lot more than anybody else here?

I wont argue with you and accept you as correct.

sid

Poll: Does 0.99 Recurring = 1

Does 0.99 Recurring = 1

Yes

No

Capodecina