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Geek Culture / Strange Maths Facts

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andrew11
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Posted: 28th May 2004 01:22 Edited at: 28th May 2004 01:22
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#constant PI 3.14159265358
Best youll ever need.

"All programmers are playwrites and all computers are lousy actors" -Anon
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Ian T
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Posted: 28th May 2004 01:29
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Undefined and infinity are different mathematical concepts .

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Chris K
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Posted: 28th May 2004 01:41
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Something I find hard to believe:

Imagine a piece of string wrapped once round the whole world, touching the floor. Now imagine it is lifted off the ground the whole way around 1 metre. The string obviously wouldn't reach any more, but how much would you need to add in order to make it reach again?

Have a guess then see what the answer is:

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Tomy
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Posted: 28th May 2004 01:48 Edited at: 28th May 2004 01:56
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Quote: "part, lets rewrite it shall we?


(16) = (16), true
(4 + 12) = (16), true
((4 - 12)-24) = ((16 - 24)-24), true
(((4 - 12) + 9) + 9) = (((16 - 24) + 9) + 9), true
((2 - 3)^2) = ((4 - 3)^2), true
sqrt((2 - 3)) = sqrt((4 - 3)), illegal, there's no sqrt for -1 you're NOT taking the sqrt from 2-3! You're taking the sqrt from (2-3)^2!
(2 + 3) = (4 + 3), false
last one (2 versions)
(1 / 2) = (2 / 2), false (1 / 2) = 0.5
(1) = (2 / 2), true, but then its 1 = 1
"


i think your wrong emperor, cuz your not taking the sqrt from -1 you're taking the sqrt from -1^2 which is positive.

The problem is the following:

Quote: "
16 = 16 Reflexive property of "="
4 + 12 = 16 From definition of "+"
4 - 12 = 16 - 24 Subtract 24 from both sides
4 - 12 + 9 = 16 - 24 + 9 Add 9 to both sides, completing squares
(2 - 3)^2 = (4 - 3)^2 Factor, rewriting as squares
2 - 3 = 4 - 3 Sqrt of each side => sqrt(x^2) is NOT x, IT'S +/- x, so both sides are +/- 1
2 = 4 Add 3 to each side
1 = 2 Divide by 2
"


----------------------

Quote: "
1/@ = 0
"


Mathematicly seen this is incorrect, because it's not defined...


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Emperor Baal
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Posted: 28th May 2004 01:56
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But still, 1 cannot be 2.

(If it is, then I hope it happens with my money )

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andrew11
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Posted: 28th May 2004 01:58
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Yeah... The point it that there is a flaw in every "proof" of 2 = 1.

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Tomy
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Posted: 28th May 2004 01:58
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LOL


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Emperor Baal
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Posted: 28th May 2004 03:46 Edited at: 28th May 2004 03:47
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Okay, why don't you solve this math problem for me?

Example of table of 1x1 and table of 2x2

[1]

Product of Rows = 1
Product of Columns = 1
Total = 2

[2][3]
[4][1]

Product of Rows = 10
Product of Columns = 11
Total = 21


Now I want you to fill in a table of 3

[x][x][x]
[x][x][x]
[x][x][x]

Product of rows = ?
product of columns = ?
Total = 436

Note: The numbers range from 1 to 9

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Dave J
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Posted: 28th May 2004 07:52
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Quote: "NO NO NO
http://mathforum.org/epigone/comp.soft-sys.math.mathematica/grencongstar

Read third message"


Nearing the end of that message it reads: "Likewise any number divided by zero is undefined (infinite).", which kind of shows they're interchangable as Chris Knott explained. Are you trying to prove yourself wrong by showing us that?


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Chris K
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Posted: 28th May 2004 11:24
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http://mathworld.wolfram.com/DivisionbyZero.html
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flibX0r
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Posted: 28th May 2004 13:11 Edited at: 28th May 2004 13:17
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None of you people ever did calculus did you?

A number divied by zero can be 0, 1 or infinity.
Heres how:
0 * x/0 : Any number multiplied by zero is zero
0/0 = 1/1 : A number divided by itself is one
1/0 : A number divided by zero is infinity (undefined)

It all depend on the context for the equation. The 3 main example of this are:

y = 1/x : When x is 0, y is +/- infinity
y = (x^2)/x : When x is 0, the limit of y would be 0, but it is undifined
y = (sin x)/x : when x is 0, the limit of y would be 1, but is also undefined.


Also...
The square root of -1 if i, the imaginary number, and is used a fair bit in calculus.


Also, you can't treat infinity as a number, it is a concept. The laws of mathematics do not apply to it. you cannot add, subtract, multiply or divide it. It is not an actual number. Its not imaginary either, because imaginary numbers are the 2nd dimension of the number line.


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Dave J
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Posted: 28th May 2004 13:29 Edited at: 28th May 2004 13:29
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Quote: "The square root of -1 if i, the imaginary number, and is used a fair bit in calculus."


It's used even more in Complex Numbers.


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Rob K
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Posted: 28th May 2004 14:51
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2+2=5 for exceedingly large values of 2.

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TKF15H
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Posted: 28th May 2004 15:58
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Ok, this one got me a bit confused. By ADDING a bunch of positive numbers, the answere is -1.

S=(1+2+4+8+16+32+.....)
S=1+(2+4+8+16+32+...)
S=1+2.(1+2+4+8+16+32+...)
S=1+2.S
S-2.S=1
-S=1
S=-1

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spooky
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Posted: 28th May 2004 16:07
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@Emperor Baal

There are loads of solutions to your puzzle. Here's a little proggy that will generate an answer in a second or so:




Boo!
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flibX0r
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Posted: 28th May 2004 16:15
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@Exeat

And currently in the TEE, complex numbers are covered in calculus

@Rob K

lmao


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Emperor Baal
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Posted: 28th May 2004 17:53
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oh spooky, you're so smart

Lets try this 10x10 FIXED one then:

[63][x][x][x][x][x][x][x][x][x]
[x][x][x][x][x][x][x][x][x][x]
[x][x][x][x][x][x][x][x][x][x]
[x][x][x][x][x][x][x][x][x][x]
[x][x][x][x][x][x][x][x][x][x]
[x][x][x][x][27][x][x][x][x][x]
[x][x][x][x][x][x][x][x][x][x]
[x][x][x][x][x][x][x][x][x][x]
[x][x][x][x][x][x][x][x][x][x]
[x][x][x][x][x][x][x][x][x][55]

Total: 125,322,878,648,283,120

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Ian T
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Posted: 28th May 2004 18:00
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1 ar teh MATH PIRATE 1 st33l ur sk1llz!!!!11

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Powersoft
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Posted: 28th May 2004 19:50
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never new maths could be so interesting

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Jeku
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Posted: 28th May 2004 19:57
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Dumb question: Why is it everyone call it maths? I've always known it as just plain math. There's no plural---- is there?

Could be an accent thing.

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Powersoft
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Posted: 28th May 2004 20:00
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maths=mathematics

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Peter H
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Posted: 28th May 2004 20:01
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maybe the title of this thread should have been "false maths facts"


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Powersoft
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Posted: 28th May 2004 20:03
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damn slipped up there.
yeah buy the way that previous 1=2 thoery is WRONG

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Peter H
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Posted: 28th May 2004 20:12
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yes we figured that out.
the problem was that they took the square root of -1 which is impossible.(you can use i if you want...)


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TheAbomb12
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Posted: 28th May 2004 20:17 Edited at: 28th May 2004 20:39
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Quote: "0/0 = 1/1 : A number divided by itself is one"


nope, see below; I explain this

Quote: "A number divied by zero can be 0, 1 or infinity."


simply not true. there are a few exceptions when dealing with polynomials; I can show you an example, but Id have to dig out my calculus book.

Quote: "you cannot add, subtract, multiply or divide [infinity]."


yes, actually you can; there is a whole section of mathmatics that deals only with infinity and its wierdness.
-----------------------
ok I was wrong, 0/0 isn't infinty, its a whole other concept.

take for instance...

a/b = c

a = b = 0, but lets not add them in yet; this is perfectlly fine, but lets rearrange it...

a = c * b

now lets substitute in a and b...

0 = c * 0

now the answer to our question is: What value of c produces a value of 0 when multiplied with 0.

well it is...

0 = 154 * 0
154 is the answer to 0/0

0 = -2492 * 0
-2492 is the answer to 0/0

0 = 1,000,000 * 0
1,000,000 is the answer to 0/0

you see ALL numbers in the complex number system can be "c", therefore the answer to 0/0 is ALL numbers in the complex number system (integers, real, imaginary, etc)


------------------------

Quote: "1/@ = 0


Mathematicly seen this is incorrect, because it's not defined..."


no, not really...you need to take the limit of the funtion...

@ = infinity (cause I don't want to keep typing it over and over)

limit f(x) = 1/x
x -> @

ok this basically says, as x approches infinity what does f(x) become closer and closer too. if you take a large number of x, you get a small value for f(x), if you take an even larger value of x you get a smaller value of f(x); if you keep on increasing the number, f(x) gets closer and closer to 0. Since we cannot test the *actual* value of infinity, we can infer that since all the large numbers less then infinity get closer to 0 each time, f(x) will become 0 when it "reaches" infinity.

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IanM
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Posted: 28th May 2004 20:53
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Not really - I simply infer that the result can become infinitely small and ever closer to zero, but never actually reach zero.

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TheAbomb12
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Posted: 28th May 2004 21:04
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Quote: "Not really - I simply infer that the result can become infinitely small and ever closer to zero, but never actually reach zero."


my "large values" of x can never reach 0, but when x is infinity it meets that asymtotic point.

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Ian T
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Posted: 28th May 2004 22:03
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'Maths' also annoys me. 'Math' has been the formal abbreviation of mathematics for, what, centuries now?

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TheAbomb12
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Posted: 28th May 2004 22:22
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Quote: "'Maths' also annoys me. 'Math' has been the formal abbreviation of mathematics for, what, centuries now?"


who cares?

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Peter H
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Posted: 28th May 2004 23:52
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i do

maths sounds so trendy


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Tomy
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Posted: 29th May 2004 01:40 Edited at: 29th May 2004 01:41
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Quote: "yes we figured that out.
the problem was that they took the square root of -1 which is impossible.(you can use i if you want...)"


No that wasn't the problem as i said!
The problem was that sqrt(x^2) = +/- x and NOT x
ie. what is sqrt(9)?? if i just asked that without mentioning anything b4, most ppl would've said 3, which however is FALSE!
sqrt(9) = +/- 3!
And that was the problem in the 2=1 "proof"

Another time for you:
Quote: "
16 = 16 Reflexive property of "="
4 + 12 = 16 From definition of "+"
4 - 12 = 16 - 24 Subtract 24 from both sides
4 - 12 + 9 = 16 - 24 + 9 Add 9 to both sides, completing squares
(2 - 3)^2 = (4 - 3)^2 Factor, rewriting as squares
2 - 3 = 4 - 3 Sqrt of each side
2 = 4 Add 3 to each side
1 = 2 Divide by 2
"


all the bold things are wrong!

This one would be correct:
Quote: "
16 = 16 Reflexive property of "="
4 + 12 = 16 From definition of "+"
4 - 12 = 16 - 24 Subtract 24 from both sides
4 - 12 + 9 = 16 - 24 + 9 Add 9 to both sides, completing squares
(2 - 3)^2 = (4 - 3)^2 Factor, rewriting as squares
2-3=3-4 OR 3-2=4-3
+/- 1 = +/- 1
0=0
"



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Jeku
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Posted: 29th May 2004 03:39
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Quote: "who cares?"


I do, which is the reason why I posted the question.

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IanM
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Posted: 29th May 2004 04:30
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Is that dumb maths calculation still going? Has no-one spotted the real reason that it's wrong? Still?

Oh dear ...

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Dave J
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Posted: 29th May 2004 05:22
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Quote: "Dumb question: Why is it everyone call it maths? I've always known it as just plain math. There's no plural---- is there?"


Because as previously stated, it stands for Mathematics so dropping the 's' makes it sound incorrect, saying 'Math' would essentially be equal to saying 'Mathematic' which sounds odd IMHO. I also believe Math to be an american thing, I know down here everyone calls it Maths.


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Jess T
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Posted: 29th May 2004 05:57 Edited at: 29th May 2004 06:13
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Quote: "I simply infer that the result can become infinitely small and ever closer to zero, but never actually reach zero."


Shelton, I have to agree with IanM there...

x can get extremely large, as you've said... and as it get's so much more massive, the polynomial becomes,

f(x) = 1/x
f(x) = 1/uncomprehensibly massive number

That uncomprehensible number has been given the name infinity...

infinity isn't a point, or a number, it just keeps going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going, and going... Well, you get the point.

Shelton, let's take your quote and rip it apart shall we?
Quote: "when x is infinity it meets that asymtotic point."


I say that infinity isn't a number, nor a point in time/space/anything. It is just a name we gave to identify those excedingly massive numbers that just get too freaking huge for our brains to comprehend.

Now, let's take your theory of it...
You say that it is a point ( not a number though )... It is a point somewhere, be it in space, in time, or on a number line.

And as you said, at infinity, the polynomial finally reaches that asymtopte.

This is not possible, as the polynomial never actually get's there...

*If* it was possible, you could plot that polynomiial on a number plain ( without a limited Domain or Range ), and look at it... It gets so very, very close to that asymtopte, but never, ever reaches it.

At this infinity point, you say that it is undefined, and is therefore 0 ( as 0 is undefined ), but that relation is not sustainable, because there is NO relation between infinity and 0.

Maybe in extremely high level math, infinity may be taken as 0 to help with an equation... But that's just for convenience, and when someone says "but that can't work" they have the discussion we're having now.

This just show's how we humans invented Math... the world would keep turning if 2 = 1, if Pi = 9.54, or if the diameter of the sun was only 3cm... Everything is relative, and to us, our "Math" system ( particularily the parts we're talking about here ) was made up so that we could have something semi-tangable ( I say semi-tangable, cos you can't actually touch math, lol ) for our minds to play with, and "understand"...

It's quite easy to say that the "laws" ( again, things that we made up ) of the universe must hold true... But, due to our math, we don't allow anything but the laws to hold true ( this is how we based the systems ), and thus, we cannot prove that these laws are false without first redefining our math system.

Ok, I don't know how much I repeated myself there, o rhow much sense that made, but that's my views... Oh, and it's kinda early here too, so my brains not functioning on the top level.

Jess.

[EDIT]
About that dumb thing trying to prove 2 = 1, you can't just go from;
(2 - 3)^2 = (4 - 3)^2
to;
2 - 3 = 4 - 3

You must evaluate what's inside the braces first...

ie,
(2 - 3)^2 = (4 - 3)^2
-1^2 = 1^2
thus,
Sqrt((-1)^2) = Sqrt(1^2)
Then, again, you MUST evaluate what's inside the braces,
Sqrt(1) = Sqrt(1)
therefore,
+/- 1 = +/- 1




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Proteus
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Posted: 29th May 2004 07:09 Edited at: 29th May 2004 07:18
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X > 0
Y= 0.0
"X/Y"

It's really UNDEFINED, but you can say that when Y tends to ZERO+ (closing on 0 by positive numbers) then X/Y will tend to +infinity else if Y tends to ZERO- (closing on 0 by negative numbers) then X/Y will tend to -Infinity

I don't think we really need epsilons and deltas here right?

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Posted: 29th May 2004 07:28
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Proteus, Yeah, that's what I was trying to say, lol.

Jess.


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TheAbomb12
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Posted: 29th May 2004 09:27 Edited at: 29th May 2004 10:32
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[edit] See next post as this explaination is wrong.



this view is flawed because I have temporarily overlooked the fact that 0 isn't actually a value, it is nothing, and as such, even a number that is incomprehensibly small cannot equal nothing.

[edit]

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TheAbomb12
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Posted: 29th May 2004 10:21
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ok, you guys are right. I did some reseach and worked it out...

1/infinity is approx. = to 0 but not 0.

it is rather the recipricol of infinity and is SO infinitly small that it might as well be 0, but isn't.

we can never reach this recipricol in the same sense that we can never reach infinity...there is always a number smaller then it, but it is never "nothing" (0).

-----

Rules of Infinity

I = infinity
R = finite real number

non-zero R/ 0 = I
R /I = Recipricol of Infinity (1/I)
0 / 0 = all numbers in the number system
0 / I = 0
0 * I = 0

I * I = I
I * R = I
I + I = I
I + R = I

I - I = 0
I / I = 1

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Posted: 29th May 2004 12:00
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Exactly


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Powersoft
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Posted: 29th May 2004 12:45
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1=0.999999999999999999999999999999999999999999999999

x=0.99999
10x=9.9999
9x=10x-x
=9
x=9x/9
x=1

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Powersoft
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Posted: 29th May 2004 12:50
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just realised someone else posted this

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David T
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Posted: 29th May 2004 17:41
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Quote: "1=0.999999999999999999999999999999999999999999999999

x=0.99999
10x=9.9999
9x=10x-x
=9
x=9x/9
x=1"


Quote: "just realised someone else posted this"


Lol, about to say the same thing :p

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Peter H
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Posted: 29th May 2004 18:16
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you guys have to much time on your hands


Formerly known as "DarkWing Duck"
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Jess T
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Posted: 29th May 2004 18:34
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Hey man, back off or I'll hunt you down and steal your dog!



Jess.


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Tomy
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Posted: 29th May 2004 21:31 Edited at: 30th May 2004 06:53
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Quote: "[EDIT]
About that dumb thing trying to prove 2 = 1, you can't just go from;
(2 - 3)^2 = (4 - 3)^2
to;
2 - 3 = 4 - 3

You must evaluate what's inside the braces first...

ie,
(2 - 3)^2 = (4 - 3)^2
-1^2 = 1^2
thus,
Sqrt((-1)^2) = Sqrt(1^2)
Then, again, you MUST evaluate what's inside the braces,
Sqrt(1) = Sqrt(1)
therefore,
+/- 1 = +/- 1
"


Which is just exactly what i said!

[EDIT]oh wait:

Quote: "You must evaluate what's inside the braces first...
"


That's not a 100% true (but 99.9%), because if you have ie:

sqrt(x^2)=sqrt(y^2)

according to you, you couldn't simplify this, because you don't know whether x or y are positive or negative... however the right solution would be:

+/- |x| = +/- |y|

so in this example:

+/- |(2-3)| = +/- |(4-3)|
so +/- 1 = +/- 1

lol but you were correcter than me


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ReD_eYe
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Posted: 29th May 2004 23:35
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yeah, i'd have to agree with what you all just said...
*nods and smiles with blank, confused look on his face*

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IanM
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Posted: 29th May 2004 23:44
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@Tomy, That's not what he means at all.

What he means is that applying a square root to each side of the equation is not a legal manipulation of the equation. Applying a square root to each side is exactly like dividing each side by a different value, unless the values within the square root are exactly the same.

Basically, you can add, subtract, multiply or divide, but not apply a square root.

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Tomy
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Posted: 30th May 2004 06:49 Edited at: 30th May 2004 16:21
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But yes you can apply square root to each side, you just mustn't forget the abs!!
as i said

x^2=y^2 | sqrt()
+/- |x| = +/- |y| or in db style +/- abs(x) = +/- abs(y)

And saying you CANNOT apply a square root to each side is actually wrong...

Quote: "Applying a square root to each side is exactly like dividing each side by a different value"


no, you divide each side by the same value because |x|=|y| and -|x|=-|y|

Quote: "applying a square root to each side of the equation is not a legal manipulation of the equation."


wrong... it is legal but not in the way it is used in the "1=2-proof"...


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Jess T
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Posted: 30th May 2004 08:33
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Yeah, what I was saying is that you can't just say, ok, so there's an equation inside the braces, and that equation is being put the power of 2... so, to get rid of that, let's take the square root of both sides... - that's not fully correct, because that particular equation is fully numeric, no variables involved, thus, you must first evaluate the braces, THEN you can put it to the power of 2, or alternatively you can take the root of both sides, which is just plain pointless...

The equation should read like this:
16 = 16
4 + 12 = 16
4 - 12 = 16 - 24
4 - 12 + 9 = 16 - 24 + 9
(2 - 3)^2 = (4 - 3)^2
-1^2 = 1^2
1 = 1

and voila! Solved

As has already been said, all these stupid proof's have flaws in them, and, as I said early, that's because of our math system.

Jess.


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