|
Author
|
Topic: A question of numbers (one for the maths fans)
|
kuresu
Member (Idle past 2541 days) Posts: 2544 From: boulder, colorado Joined: 03-24-2006
|
|
Message 56 of 215 (325509)
06-23-2006 11:27 PM
|
Reply to: Message 53 by riVeRraT
06-23-2006 8:20 PM
|
|
Re: yum yum
But pi is different from an infinetly repeating decimal. It is an infinetly nonrepeating decimal, which makes it irrational. This is the problem pythagoras ran into in Greece--they didn't like the concept of an irrational number (if I've got my history right). You can't write pi as a fraction, but you can .3333 to inifity.
All a man's knowledge comes from his experiences
| This message is a reply to: | | | Message 53 by riVeRraT, posted 06-23-2006 8:20 PM | | riVeRraT has not replied |
| Replies to this message: | | | Message 57 by jar, posted 06-23-2006 11:32 PM | | kuresu has replied |
|
kuresu
Member (Idle past 2541 days) Posts: 2544 From: boulder, colorado Joined: 03-24-2006
|
|
|
Message 61 of 215 (325517)
06-23-2006 11:56 PM
|
Reply to: Message 57 by jar
06-23-2006 11:32 PM
|
|
Re: yum yum
The babylonian number system is based off of 6, which doesn't present a problem with pi then (if I remember correctly). I don't know what number the egyptians number system was based off of. And that's a whole cultural thing with ancient greece, I believe. Different cultures, different acceptances.
All a man's knowledge comes from his experiences
| This message is a reply to: | | | Message 57 by jar, posted 06-23-2006 11:32 PM | | jar has not replied |
|
kuresu
Member (Idle past 2541 days) Posts: 2544 From: boulder, colorado Joined: 03-24-2006
|
|
|
Message 64 of 215 (325520)
06-23-2006 11:59 PM
|
Reply to: Message 62 by riVeRraT
06-23-2006 11:56 PM
|
|
Re: Saucy numbers
The infinity symbol is a sideways 8.
All a man's knowledge comes from his experiences
| This message is a reply to: | | | Message 62 by riVeRraT, posted 06-23-2006 11:56 PM | | riVeRraT has replied |
| Replies to this message: | | | Message 67 by riVeRraT, posted 06-24-2006 12:05 AM | | kuresu has not replied | | | Message 68 by jar, posted 06-24-2006 12:07 AM | | kuresu has not replied |
|
kuresu
Member (Idle past 2541 days) Posts: 2544 From: boulder, colorado Joined: 03-24-2006
|
|
|
Message 66 of 215 (325523)
06-24-2006 12:05 AM
|
Reply to: Message 63 by riVeRraT
06-23-2006 11:58 PM
|
|
0.999999 to infinity is not infinity. It is 1. Inifinty could be described as a number that never ends. So it would have to be 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 ad infinitem. Once you put a decimal place in there, it stops being an infinite number. Infinity is very important in describing graphs. And most likely a whole range of other problems. Like the size of the universe. Or God's power.
All a man's knowledge comes from his experiences
| This message is a reply to: | | | Message 63 by riVeRraT, posted 06-23-2006 11:58 PM | | riVeRraT has replied |
| Replies to this message: | | | Message 70 by riVeRraT, posted 06-24-2006 12:08 AM | | kuresu has not replied |
|
kuresu
Member (Idle past 2541 days) Posts: 2544 From: boulder, colorado Joined: 03-24-2006
|
|
|
Message 72 of 215 (325530)
06-24-2006 12:14 AM
|
Reply to: Message 65 by riVeRraT
06-24-2006 12:04 AM
|
|
Re: infinities work fine
Try this objective proof on for size, by the very same Galileo that angered the church.
Galileo's para-
dox.
1 2 3 4 5 6 7 . . .
1 4 9 16 25 36 49 . ..
The paradoxical situation arises because, on the one hand, it seems
evident that most natural numbers are not perfect squares, so that the
set of perfect squares is smaller than the set of all natural numbers; but,
on the other hand, since every natural number is the square root of ex-
actly one perfect square, it would seem that there are just as many per-
fect squares as natural numbers. For Galileo the upshot of this paradox
was that, "we can only infer that the totality of all numbers is infinite,
and that the number of squares is infinite . . . ; neither is the number
of squares less than the totality of all numbers, nor the latter greater
than the former; and finally, the attributes 'equal,' 'greater,' and 'less,'
are not applicable to infinite, but only to finite quantities." One of the better math people here will have to explain it. I understand what's written here, but I can't explain it. This proof isn't under the current use (or proof?) of infinity, but was an important step in establishing that infinity does indeed exist (much to the chargin of the ancient greek metaphysicians) ABE: forgot the source. Here it is: http://www.math.yorku.ca/...s/3500/Infinity/iatmChapter1.txt Edited by kuresu, : No reason given.
All a man's knowledge comes from his experiences
| This message is a reply to: | | | Message 65 by riVeRraT, posted 06-24-2006 12:04 AM | | riVeRraT has replied |
|
kuresu
Member (Idle past 2541 days) Posts: 2544 From: boulder, colorado Joined: 03-24-2006
|
|
|
Message 75 of 215 (325534)
06-24-2006 12:18 AM
|
Reply to: Message 73 by riVeRraT
06-24-2006 12:15 AM
|
|
Re: Saucy numbers
Doesn't a circle go on for forever? After all, where does it begin, and where does it end? How's that for a proof?
All a man's knowledge comes from his experiences
| This message is a reply to: | | | Message 73 by riVeRraT, posted 06-24-2006 12:15 AM | | riVeRraT has replied |
| Replies to this message: | | | Message 77 by riVeRraT, posted 06-24-2006 12:20 AM | | kuresu has replied |
|
kuresu
Member (Idle past 2541 days) Posts: 2544 From: boulder, colorado Joined: 03-24-2006
|
|
|
Message 80 of 215 (325540)
06-24-2006 12:28 AM
|
Reply to: Message 76 by riVeRraT
06-24-2006 12:19 AM
|
|
Re: infinities work fine
we all agree that the symbol for one, 1, stands for there being one item, object, whatever. Like when you're a kid, and the elementary teacher in the first grade teaches you how to add by using boxes. You have three boxes. Add two boxes. You now have five boxes. That's how one is objective. In fact, the whole number system is objective. Try looking at Galileo's paradox, which I posted just a short while ago. Totally objective--you can't escape the logic inherent in math.
All a man's knowledge comes from his experiences
| This message is a reply to: | | | Message 76 by riVeRraT, posted 06-24-2006 12:19 AM | | riVeRraT has not replied |
|
kuresu
Member (Idle past 2541 days) Posts: 2544 From: boulder, colorado Joined: 03-24-2006
|
|
|
Message 81 of 215 (325541)
06-24-2006 12:28 AM
|
Reply to: Message 77 by riVeRraT
06-24-2006 12:20 AM
|
|
Re: Saucy numbers
Then a circle becomes a line. But so long as it's a circle, it goes on for forever.
All a man's knowledge comes from his experiences
| This message is a reply to: | | | Message 77 by riVeRraT, posted 06-24-2006 12:20 AM | | riVeRraT has replied |
| Replies to this message: | | | Message 87 by riVeRraT, posted 06-24-2006 12:47 AM | | kuresu has not replied |
|
kuresu
Member (Idle past 2541 days) Posts: 2544 From: boulder, colorado Joined: 03-24-2006
|
|
|
Message 88 of 215 (325551)
06-24-2006 12:47 AM
|
Reply to: Message 83 by riVeRraT
06-24-2006 12:36 AM
|
|
Re: Great Rat.
On my Ti-86, the square root of 0.999999999999 (at which point the calculator recognizes that the number is forever repeating), it is 1. However, it refuses to turn the same number into 1 when asked to turn the number into a fraction.
All a man's knowledge comes from his experiences
| This message is a reply to: | | | Message 83 by riVeRraT, posted 06-24-2006 12:36 AM | | riVeRraT has not replied |
|
kuresu
Member (Idle past 2541 days) Posts: 2544 From: boulder, colorado Joined: 03-24-2006
|
|
|
Message 90 of 215 (325554)
06-24-2006 12:54 AM
|
Reply to: Message 83 by riVeRraT
06-24-2006 12:36 AM
|
|
Re: Great Rat.
let's take this number. 3.12341234123412341234123412341234123412341234 ad infinitem. let's subtract it by 1.23352335233523352335233523352335233523352335233523352335 ad infitem. Or, we can just write it as 3.1234 - 1.2335, and write the repeat symbol over it. So it's 1.8899, with the 8899 having an (overscore?) written over it. Nothign logically wrong with it. I mean, after all, 1 is really just 1.000000000000000000000000000000000000000000000 ad infitem, and zero is recognized as a number, right?
All a man's knowledge comes from his experiences
| This message is a reply to: | | | Message 83 by riVeRraT, posted 06-24-2006 12:36 AM | | riVeRraT has not replied |
|
kuresu
Member (Idle past 2541 days) Posts: 2544 From: boulder, colorado Joined: 03-24-2006
|
|
|
Message 101 of 215 (325649)
06-24-2006 11:34 AM
|
Reply to: Message 95 by lfen
06-24-2006 2:47 AM
|
|
Re: Zeno's motion paradoxes and the sum of infinite series, the calculus
Zeno's problem is that he assumes that man runs like the graph of a square root, or maybe more precisely, runs like the value e 
All a man's knowledge comes from his experiences
| This message is a reply to: | | | Message 95 by lfen, posted 06-24-2006 2:47 AM | | lfen has not replied |
|
kuresu
Member (Idle past 2541 days) Posts: 2544 From: boulder, colorado Joined: 03-24-2006
|
|
|
Message 105 of 215 (325841)
06-24-2006 9:03 PM
|
Reply to: Message 104 by riVeRraT
06-24-2006 8:28 PM
|
|
Re: Great Rat.
On my Ti-86, a number with twelve decimal places is assumed to go on for inifinity. So .999999999999 stretches on for infinity, as should pi (but my calculator stops at eleven for some reason). Anywho, .999999999999 / 2 = .5. So, .5 *2 = 1 or .999999999999 again, my calculator considers 12 decimal places to strech for infinity, so I have twelve for the decimals here (except .5, of course)
All a man's knowledge comes from his experiences
| This message is a reply to: | | | Message 104 by riVeRraT, posted 06-24-2006 8:28 PM | | riVeRraT has not replied |
|
kuresu
Member (Idle past 2541 days) Posts: 2544 From: boulder, colorado Joined: 03-24-2006
|
|
|
Message 109 of 215 (325878)
06-24-2006 10:06 PM
|
Reply to: Message 108 by riVeRraT
06-24-2006 9:58 PM
|
|
I can't remember if modulus used the .333 . . . or not. 3.333 . . . is not 3. It's 10 / 3 QUite naturally, 1 does not equal 1 / 3. (unless they are the zeroes of the equation ) Where are you getting x = 1? You have no math in this post to support that. I know from the matter we've been dealing with, x has been 1, but that was dealing with .999 . . .. Now you have a new number, and as such, a new variable.
All a man's knowledge comes from his experiences
| This message is a reply to: | | | Message 108 by riVeRraT, posted 06-24-2006 9:58 PM | | riVeRraT has not replied |
|
kuresu
Member (Idle past 2541 days) Posts: 2544 From: boulder, colorado Joined: 03-24-2006
|
|
|
Message 111 of 215 (325884)
06-24-2006 10:19 PM
|
Reply to: Message 110 by nwr
06-24-2006 10:14 PM
|
|
A s mall slip there small slip indeed.  sorry, couldn't stop laughing when I read that. but then, I'm easily amused, so . . . ABE: of course, I make that kind off mistake a lot too. Edited by kuresu, : No reason given.
All a man's knowledge comes from his experiences
| This message is a reply to: | | | Message 110 by nwr, posted 06-24-2006 10:14 PM | | nwr has not replied |
|
kuresu
Member (Idle past 2541 days) Posts: 2544 From: boulder, colorado Joined: 03-24-2006
|
|
|
Message 118 of 215 (325906)
06-24-2006 10:49 PM
|
Reply to: Message 115 by riVeRraT
06-24-2006 10:40 PM
|
|
infinity +1 ? or - 1?
What does it equal?
Just that.
In the equation 10 x .999 = 9.99 In this equation, it's assumed that the nines go on for infinity (that's how it's been treated in this entire thread. So move the decimal place, and you've still got an infinite number of nines following the decimal place.
All a man's knowledge comes from his experiences
| This message is a reply to: | | | Message 115 by riVeRraT, posted 06-24-2006 10:40 PM | | riVeRraT has replied |
| Replies to this message: | | | Message 121 by riVeRraT, posted 06-24-2006 11:12 PM | | kuresu has replied |
|
™ Version 4.2