Is 1 = 0.9999......

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mchammer187

Diamond Member
Nov 26, 2000
9,114
0
76
Originally posted by: cheapbidder01
Originally posted by: mchammer187
Originally posted by: Shanti
Everyone who's taken calculus should know that it approaches one but isn't equal to one.

everyone who has taken calculus and UNDERSTOOD it would realize that .9999...... is not a limit thus it cannot approach anything other than what it is 1

plot y= .999999999999999999.............. if it has a different value @ x = infinity than x=0 something is seriously wrong

You didn't understand calculus did you. You didn't do your plot right either, if you didn't get Y=1 for any X.

I understood calc very well thank you

y = 1 for all values of x thus it does not approach anything that it already is for ALL VALUES
 

AgaBoogaBoo

Lifer
Feb 16, 2003
26,108
5
81
I'm glad I haven't ever tried reading this thread, if I did, it would take many hours to catch up, I haven't even read the first page :Q
 

silverpig

Lifer
Jul 29, 2001
27,703
12
81
Originally posted by: RossGr
9 + .09 + .009 + ... = Sum N{1,M} [9*.1^N] = B


I disagree. you have presened a recognizable pattern followed by an ellipsis. This means I should continue the pattern infinitly. What you have represented is = .999... . The sum does not terminate at some unspecificed M, it continues to infinity.

How then would you write Sum N{1,M} [9*.1^N] in discrete terms? .9 + .09 + .009 + ... + .{M-1,0}9?

The only time I use an ellipsis to refer to infinity is as in 0.999... otherwise it makes sense to have it mean some arbitrary number. Very formally you can't have a sum of an infinite number of terms, but only a limit of an arbitrary number of terms as that arbitrary upper limit approaches infinity. ie:

Sum N{1,inf} x

is just informal shorthand for

lim m->inf Sum N{1,m} x

Either way though, this is just a matter of notation and not of real mathematical substance. The final point is that the number 0.999... is the limit of the sum, and is equal to 1. Notation aside, the ideas are there.
 

silverpig

Lifer
Jul 29, 2001
27,703
12
81
Originally posted by: mchammer187
Originally posted by: Shanti
Everyone who's taken calculus should know that it approaches one but isn't equal to one.

everyone who has taken calculus and UNDERSTOOD it would realize that .9999...... is not a limit thus it cannot approach anything other than what it is 1

plot y= .999999999999999999.............. if it has a different value @ x = infinity than x=0 something is seriously wrong

It IS a limit dude. A limit is a number, an infinite sum is a progression. The limit is 1 and cannot change. To paraphrase a funny joke:

lim m->inf Sum N{1,m} 9*.1^N = 1, even for small values of infinity.

 

mchammer187

Diamond Member
Nov 26, 2000
9,114
0
76
Originally posted by: silverpig
Originally posted by: mchammer187
Originally posted by: Shanti
Everyone who's taken calculus should know that it approaches one but isn't equal to one.

everyone who has taken calculus and UNDERSTOOD it would realize that .9999...... is not a limit thus it cannot approach anything other than what it is 1

plot y= .999999999999999999.............. if it has a different value @ x = infinity than x=0 something is seriously wrong

It IS a limit dude. A limit is a number, an infinite sum is a progression. The limit is 1 and cannot change. To paraphrase a funny joke:

lim m->inf Sum N{1,m} 9*.1^N = 1, even for small values of infinity.


ok it technically is a limit

in the sense that (limit 2) = 2 as x -> any number

i was just trying to say the value of .999999999999999999999999 does not change for any value of X so therefore it does not approach anything

or it does in the sense that y = 2 approaches 2 for all values of x but that still means it holds the same value everywhere
 

bleeb

Lifer
Feb 3, 2000
10,868
0
0
If 1 = 0.99999... then why don't we see more 0.9999... McValue meals at McDonalds? Or 0.9999.. deals elsewhere? Since they are the same, shouldn't we see more 0.9999.. deals going???

0.9999... != 1!
 

Chu

Banned
Jan 2, 2001
2,911
0
0
Originally posted by: bleeb
If 1 = 0.99999... then why don't we see more 0.9999... McValue meals at McDonalds? Or 0.9999.. deals elsewhere? Since they are the same, shouldn't we see more 0.9999.. deals going???

0.9999... != 1!

For the same reason you don't see "Now on sale! New value meals for only -(($0.01)^-100)-1.99 cents! We like nice round numbers because our brain is better equipped to deal with them. In the sciences you run into limits all over the place, and the whole argument we are having about 0.9999=1 is based on people not understanding what limits are.

-Chu
 

Kyteland

Diamond Member
Dec 30, 2002
5,747
1
81
Originally posted by: bleeb
If 1 = 0.99999... then why don't we see more 0.9999... McValue meals at McDonalds? Or 0.9999.. deals elsewhere? Since they are the same, shouldn't we see more 0.9999.. deals going???

0.9999... != 1!

Man Bleeb. if you keep bumping this post there's going to be a ATOT lynching.

"String him up, and make sure the rope is 0.9999.... feet long!!"

I don't know about you, but I've had the 0.9999... McValue meal before. You must go to the wrong McDonalds if you've never had it.
 

BigToque

Lifer
Oct 10, 1999
11,700
0
76
Theoretically, 1 != .999...
Practically, 1 = .999...

I can't imagine some carpenter saying "Damnit Jim, you cut the fscking board to short! I said 1 meter, not .999999999999999999999999999999999 meters! Get it right!

How this reached 1900 posts is beyond me.
 

jurzdevil

Golden Member
Feb 3, 2002
1,258
0
0
Originally posted by: bigredguy
FOR THE LOVE OF GOD LET THIS DIE. I BEG ALL OF YOU TO NEVER POST HERE AGAIN. My $.02

you mean your $.019999999999999999999999999999999999999999999999999
 

MAME

Banned
Sep 19, 2003
9,281
1
0
Originally posted by: bleeb
If 1 = 0.99999... then why don't we see more 0.9999... McValue meals at McDonalds? Or 0.9999.. deals elsewhere? Since they are the same, shouldn't we see more 0.9999.. deals going???

0.9999... != 1!

you can't be serious
 

BigToque

Lifer
Oct 10, 1999
11,700
0
76
Originally posted by: MAME
Originally posted by: Stefan
Theoretically, 1 != .999...
Practically, 1 = .999...

you are wrong. prove this statement

X = .999999999999999

1 - X = .000000000000001
1 - 1 = 0

.000000000000001 != 0

therefore X != 1

therefore .999999999999999 != 1

You can't look at it any other way. The 2 numbers are not the same.

I don't want to start talking about limits.
 

Kyteland

Diamond Member
Dec 30, 2002
5,747
1
81
Originally posted by: Stefan
I don't want to start talking about limits.
Then you must not want to start talking about 0.9999... because 0.99999999999999999999999999999999999999999 != 0.9999...
 

MAME

Banned
Sep 19, 2003
9,281
1
0
Originally posted by: Stefan
Originally posted by: MAME
Originally posted by: Stefan
Theoretically, 1 != .999...
Practically, 1 = .999...

you are wrong. prove this statement

X = .999999999999999

1 - X = .000000000000001
1 - 1 = 0

.000000000000001 != 0

therefore X != 1

therefore .999999999999999 != 1

You can't look at it any other way. The 2 numbers are not the same.

I don't want to start talking about limits.

congradulations! You proved that .999999999999999 != 1


THAT'S AMAZING!

Now, try this harder one:
prove that .999... != 1
 

Chumpman

Banned
Feb 26, 2003
1,389
0
0
Originally posted by: MAME
Originally posted by: Stefan
Originally posted by: MAME
Originally posted by: Stefan
Theoretically, 1 != .999...
Practically, 1 = .999...

you are wrong. prove this statement

X = .999999999999999

1 - X = .000000000000001
1 - 1 = 0

.000000000000001 != 0

therefore X != 1

therefore .999999999999999 != 1

You can't look at it any other way. The 2 numbers are not the same.

I don't want to start talking about limits.

congradulations! You proved that .999999999999999 != 1


THAT'S AMAZING!

Now, try this harder one:
prove that .999... != 1

hahahaha
 

BigToque

Lifer
Oct 10, 1999
11,700
0
76
Originally posted by: MAME
Originally posted by: Stefan
Originally posted by: MAME
Originally posted by: Stefan
Theoretically, 1 != .999...
Practically, 1 = .999...

you are wrong. prove this statement

X = .999999999999999

1 - X = .000000000000001
1 - 1 = 0

.000000000000001 != 0

therefore X != 1

therefore .999999999999999 != 1

You can't look at it any other way. The 2 numbers are not the same.

I don't want to start talking about limits.

congradulations! You proved that .999999999999999 != 1


THAT'S AMAZING!

Now, try this harder one:
prove that .999... != 1



X = .999...

1 - X = .000...0001
1 - 1 = 0

.000...0001 != 0

therefore X != 1

therefore .999... != 1

It is irrelevent how many 9's you add to the end of the number, you are only apporaching 1 and never getting there.
 

silverpig

Lifer
Jul 29, 2001
27,703
12
81
So you have a decimal point followed by an infinite number of zeros, and then a few more zeros, and then a one, and then nothing... Anything seem wrong with that?
 
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