|
Korean Job Discussion Forums
"The Internet's Meeting Place for ESL/EFL Teachers from Around the World!"
|
| View previous topic :: View next topic |
| Author |
Message |
huck
Joined: 19 Jan 2003
|
 Posted: Fri Mar 17, 2006 4:03 am Post subject: Confused by basic addition |
 |
|
So, I was lying in bed this morning, and while converting celsius to farenheit, I became stumped by basic addition.
1/2 + 1/2 = 1
.50 + .50 = 1
right? simple.
But 1/3 + 2/3 = 3/3 = 1
.33333 (repeating) + .666666(repeating) = .9999999 (repeating)
.99999 isn't 1. so is 3/3 approximately 1, and not exactly 1?
same thing with 1/9 + 8/9 = 9/9, which is supposedly 1.
but .1111111 + .88888888 = .999999999
where does the extra tick come from? |
|
| Back to top |
|
 |
tzechuk
Joined: 20 Dec 2004
|
| Posted: Fri Mar 17, 2006 4:23 am Post subject: |
|
|
1/3 = 0.333333333
2/3 = 0.666666667
Didn't anyone teach you that when you do divisions with a recurring digit at the end, if the digit is above 5, then you round it to the next number? So 6 becomes 7, 7 becomes 8 etc.... |
|
| Back to top |
|
|
huck
Joined: 19 Jan 2003
|
| Posted: Fri Mar 17, 2006 4:29 am Post subject: |
|
|
But you only round up when you're writing the approximate amount...
Technically speaking, 2/3 = .666666 (repeating) - it should be written with a bar over the 6 which shows that it repeats forever...you can call it .66667 or .67 or .6666666666667, but that's not it's true value.
just like the true value of .999999999999 isn't 1. |
|
| Back to top |
|
|
tzechuk
Joined: 20 Dec 2004
|
| Posted: Fri Mar 17, 2006 4:35 am Post subject: |
|
|
Well, the way it was explained to me when I ws doing maths at school was that by the time you rounded the last digit up, the actual value of that last number is so insignificant that it really doesn't matter that it is rounded up.
But if you want to nitpick, go ahead. |
|
| Back to top |
|
|
riley
Joined: 08 Feb 2003
Location: where creditors can find me
|
| Posted: Fri Mar 17, 2006 4:56 am Post subject: |
|
|
All I'm going to say is,
you're a philosophy major, right Huck?
Last edited by riley on Fri Mar 17, 2006 4:57 am; edited 1 time in total |
|
| Back to top |
|
|
midgic
Joined: 14 Feb 2004
|
| Posted: Fri Mar 17, 2006 4:57 am Post subject: |
|
|
The explanation is that 0.99999999.....= 1
Most people think that 0.999999...< 1, but this isn't the case.
1/3 = 0.33333... multiply both sides by 3, and you get 3/3 = 0.99999...
so, we can see that 1 = 0.9999999....
Still not convinced?
Consider 1 - 0.9999999.....
This value is less then every positive number, but not less than zero, therefore it must equal zero.
Thus, 1 = 0.999999..... |
|
| Back to top |
|
|
huck
Joined: 19 Jan 2003
|
| Posted: Fri Mar 17, 2006 5:10 am Post subject: |
|
|
I understand what you're saying, and I'm not disagreeing with it. It's just a "wondering" question because you would assume that math wouldn't have any inequalities like this existing...it's math...it's concrete and proven...it's not like quantum physics, or even negative numbers.
But let's say I eat .333333333(repeating) of a pie, and you're a pig so you eat .66666666(repeating) of the pie......won't there still be a very small, teeny-weeny, infinitesimal speck that didn't get eaten?
Disclaimer: The "pig" remark was not directed at any one person, and it isn't meant to be derogatory. Pigs just seem like they could eat 2/3's of a pie. |
|
| Back to top |
|
|
shortskirt_longjacket
Joined: 06 Jun 2004
Location: fitz and ernie are my raison d'etre
|
| Posted: Fri Mar 17, 2006 5:20 am Post subject: |
|
|
The sum of .33333333(repeating into infinity) and the sum of .666666(repeating into infinity) isn't .999999999(repeating into infinity). It's 1. Or, rather, .9999999(repeating into infinity) = 1. It's not "approximately" one, or "nearly" 1...it's exactly 1.
Weird, but just one of the presuppositions you have to accept to adhere to the religion of mathematics (the one true religion, by the way...the religion upon which all our technology, science, and knowledge of the universe is based). |
|
| Back to top |
|
|
huck
Joined: 19 Jan 2003
|
| Posted: Fri Mar 17, 2006 5:42 am Post subject: |
|
|
Thanks...I just found this online, and I'll adopt it as my new answer if anyone ever asks me this question.
| Quote: |
No. Mathamitically speaking, they are not the same value, and hence, not truely the same amount. The differeance between the two ammounts is infinitly small, and can not be truely understood, only accepted as existing, but the differance still remains. Although the further along the nines went the closer they would get to being one, they will never actually reach one.
And Yes. For any real use, they are exactly the same, you would never nitpick over a differance of that infinitly small space between the two values.
So technically no, but in the working world, yes, they're the same bloody number. |
Last edited by huck on Fri Mar 17, 2006 5:44 am; edited 1 time in total |
|
| Back to top |
|
|
midgic
Joined: 14 Feb 2004
|
| Posted: Fri Mar 17, 2006 5:44 am Post subject: |
|
|
| Quote: |
But let's say I eat .333333333(repeating) of a pie, and you're a pig so you eat .66666666(repeating) of the pie......won't there still be a very small, teeny-weeny, infinitesimal speck that didn't get eaten?
|
The short method: We cut the pie into three pieces, I eat two of them, and you eat one. The pie is gone.
The long method: We cut the pie into ten pieces, you eat 3 pieces, and I eat six pieces. There's one piece left. Repeat the process, each time cutting what's left over into ten pieces. Thus, after the n'th repetition, you have eaten 0.3333...3333 (n 3's) of the pie, and I have eaten 0.6666...6666 (n 6's) of the pie. After each repetition, the piece left over is one tenth the size of the previous leftover piece. Unfortunately, we can't check to see if anything is left at the very end of this process, because we'll never get to the end of this process. |
|
| Back to top |
|
|
shortskirt_longjacket
Joined: 06 Jun 2004
Location: fitz and ernie are my raison d'etre
|
| Posted: Fri Mar 17, 2006 5:46 am Post subject: |
|
|
| huck wrote: |
Thanks...I just found this online, and I'll adopt it as my new answer if anyone ever asks me this question.
| Quote: |
No. Mathamitically speaking, they are not the same value, and hence, not truely the same amount. The differeance between the two ammounts is infinitly small, and can not be truely understood, only accepted as existing, but the differance still remains. Although the further along the nines went the closer they would get to being one, they will never actually reach one.
And Yes. For any real use, they are exactly the same, you would never nitpick over a differance of that infinitly small space between the two values.
So technically no, but in the working world, yes, they're the same bloody number. |
|
ugh! the spelling is so offensive! don't use that as your answer (at least in written form). it reeks of ignorance. where did you find such an ugly explanation? |
|
| Back to top |
|
|
tzechuk
Joined: 20 Dec 2004
|
| Posted: Fri Mar 17, 2006 6:02 am Post subject: |
|
|
| shortskirt_longjacket wrote: |
| huck wrote: |
Thanks...I just found this online, and I'll adopt it as my new answer if anyone ever asks me this question.
| Quote: |
No. Mathamitically speaking, they are not the same value, and hence, not truely the same amount. The differeance between the two ammounts is infinitly small, and can not be truely understood, only accepted as existing, but the differance still remains. Although the further along the nines went the closer they would get to being one, they will never actually reach one.
And Yes. For any real use, they are exactly the same, you would never nitpick over a differance of that infinitly small space between the two values.
So technically no, but in the working world, yes, they're the same bloody number. |
|
ugh! the spelling is so offensive! don't use that as your answer (at least in written form). it reeks of ignorance. where did you find such an ugly explanation? |
I quite agree! |
|
| Back to top |
|
|
ontheway
Joined: 24 Aug 2005
Location: Somewhere under the rainbow...
|
| Posted: Fri Mar 17, 2006 8:24 am Post subject: |
|
|
| In mathematics, this is basically a "limit" problem. The limit as n approaches infinity. |
|
| Back to top |
|
|
mole
Joined: 06 Feb 2003
Location: Act III
|
| Posted: Fri Mar 17, 2006 8:40 am Post subject: |
|
|
| ontheway wrote: |
| In mathematics, this is basically a "limit" problem. The limit as n approaches infinity. |
 Took me three tries to pass my required Calculus II in uni. Still gives me a headache.
My philosophy professor, though, gave an example similar to the pies above.
If you're running full speed at a brick wall, you can always cut your distance
between you and the wall by a fraction (half, for simplicity.) Will you never smash into the wall? 
Last edited by mole on Fri Mar 17, 2006 9:30 am; edited 1 time in total |
|
| Back to top |
|
|
jacl
Joined: 31 Oct 2005
|
| Posted: Fri Mar 17, 2006 9:13 am Post subject: |
|
|
There once was a man from Bengal
Who had a octangular ball
It was a fourth of his weight
Pluse his peanus, plus eight
Made a fourth of a fifth of fark all |
|
| Back to top |
|
|
|
|
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum
|
|
FAQ
Search
Memberlist
Usergroups
Register
Profile
Log in to check your private messages
Log in
