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Posted By: Tracee

Posted On: Nov 11, 2004
Views: 1093
Dumb Thought/Question I have

ok...so 1/3+2/3 of course equals 1.
1/3=.3333(infinatly)
2/3=.6666(infinatly)
but shouldn't .3333(infinatly)+ .6666(infinatly)= .9999(infinatly).
am I stupid and missing something very obvious, or isn't there something wrong with this? Does anyone understand what I am getting at? Any comments would be very helpful!!!

Posted By: Bill

Posted On: Nov 13, 2004
Views: 1091
RE: Dumb Thought/Question I have

First, there are no dumb questions. =) I see it as this... you are either approaching 1 or 0 in your description.

This is a kind of domain or range. I forget...

What you're describing is something like focusing in on one tiny particular region of the whole and focusing down infinitely. So as I see it, you're thinking about 1 dimension of infinite degrees.

Posted By: Tracee

Posted On: Nov 14, 2004
Views: 1088
RE: Dumb Thought/Question I have

Thanx for trying to answer my question, but I beleive I did a very poor job explaining exactly what my question is...let me see if I can re-explain. ok, if 1/3+2/3=1, why is it that
if 1/3=.3repeating and 2/3=.6repeating the following equation would not agree:
.3repeating+.6repeating DOES NOT equal exactly 1, but instead .9repeating.
Does this make any sense as to what I am asking, I am sure the answer is obvious, math is not my forte.

Posted By: Keith Mayes

Posted On: Nov 15, 2004
Views: 1086
RE: Dumb Thought/Question I have

Hi Tracee,
The only reason your sums do not appear to make sense is because we are making approximations when we use decimals.
Look at it in a simple way, it makes it easier to understand, and easier for me to explain.
1/3 of something is precisely one third. So divide a cake into three equal portions and each portion is exactly one third of the whole cake. If however, you decide to change your method of calculation and go decimal, it will not quite work. You can't exactly express 1/3 as a decimal, because as you say it is 0.3333333'. Therefore two slices is 0.6666666'. Because this conversion to decimal is not precise, it looks as if the sums are wrong, but they are not, its just that decimals are not fractions. The three slices still make a complete whole cake, nothing has gone missing of course, its just the degree of accuracy used is different. Fractions are exact, 1/3 means 1 divided by 3. Decimals are a more useful way of expressing and handling numbers, but technically are not as accurate.
Keith

Posted By: Tracee

Posted On: Nov 15, 2004
Views: 1082
RE: Dumb Thought/Question I have

Thank you for the explanation!

Posted By: Pyrovus

Posted On: Dec 21, 2004
Views: 1058
RE: Dumb Thought/Question I have

Actually it can be proven that .9999' exactly equals 1:

let x = .99999'
= 9/10 + 9/100 + 9/1000 + 9/10000 . . .
Multiply both sides by 10:
:. 10x= 9 + 9/10 + 9/100 + 9/1000 + 9/10000 . . .
substitute 9/10 + 9/100 + 9/1000 . . . = x:
:. 10x= 9 + x
:. 9x= 9
:. x= 1

Posted By: Keith Mayes

Posted On: Dec 21, 2004
Views: 1056
RE: Dumb Thought/Question I have



Posted By: Pyrovus

Posted On: Jan 3, 2005
Views: 1045
RE: Dumb Thought/Question I have

Except that both values of x are the same.

When we write a number, say 12,345, as a result of the way place value notation works, what we are really writing is 1x10^4 + 2x10^3 +3x10^2 +4x10^1 +5x10^0 (read 1 lot of ten thousand plus 2 lots of one thousand etc.)

Likewise, decimal numbers like .1724 can be rewritten as 1x10^-1 + 7x10^-2 + 2x10^-3 + 4x10^-4, or 1x0.1 + 7x0.01 + 2x.001 + 4x.0001, or 1/10 + 7/100 + 2/1000 + 4/10000 (.1 = 1/10, .01 = 1/100 etc). All these forms are equivalent.

Going back to .9999999'
We can write this as an infinite sum:
.9999999'=.9 +.09 +.009 +.0009 . . . forever
and as .9=9/10, .09=9/100 etc
then .999999'= 9/10 + 9/100 + 9/1000 etc

They both have the same value, even though they are written differently, much in the same way that sin(pi/2) and cos(0), both represent the same number and therefore may be interchanged.

And another thing. The interval between any two different numbers can be infinitely divided eg. there are infinitely many numbers between one and two. However, there are no numbers between 0.999' and 1, so they cannot be different numbers.

Posted By: Keith Mayes

Posted On: Jan 3, 2005
Views: 1042
RE: Dumb Thought/Question I have



Posted By: Pyrovus

Posted On: Jan 3, 2005
Views: 1039
RE: Dumb Thought/Question I have



Posted By: Pyrovus

Posted On: Jan 3, 2005
Views: 1037
RE: Dumb Thought/Question I have



Posted By: Keith Mayes

Posted On: Jan 4, 2005
Views: 1033
RE: Dumb Thought/Question I have

Good grief, you do go on and on!
Okay, I am sure you must be right.

OF COURSE 0.99999999' is equal to 1

Every idiot knows that.

Posted By: .9 repeating does NOT equal 1

Posted On: Feb 4, 2005
Views: 990
RE: Dumb Thought/Question I have

You made a fatal mistake in your theory.

1 != .999999999'

As we learn from derivatives and anti-derivatives, every time you derive you either lose a constant or add one (+ C). You failed to account for this.

Your answer should be:

3x^2 = 6x, but the anti-derivative of 6x = 3x^2 + C


Posted By: Keith Mayes

Posted On: Feb 24, 2005
Views: 960
RE: Dumb Thought/Question I have

Thanks for your confirmation that 0.99999999' does not equal 1

I am still at a loss to understand how anyone could think otherwise!

No amount of maths can make 1 equal to something that by defintion is less than 1.

Posted By: Alan

Posted On: Mar 1, 2005
Views: 948
RE: Dumb Thought/Question I have

WOAH!!! ARE YOU TRYING TO MAKE MY HEAD EXPLODE!?

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