Infinity

2006-11-29 20:05:17

#1

some_random_panda: Flamesuit essential; +454|6835

I thought that this was interesting and so i removed it from the post and put it in this one...

Say, you have infinite number of columns leading down of infinite numbers in this pattern and infinite rows of infinite numbers leading across in this pattern...

0 1 1/2 1/4 1/8 1/16... =2

-1 0 1 1/2 1/4 1/8... =1

-1/2 -1 0 1 1/2 1/4... =1/2

-1/4 -1/2 -1 0 1 1/2... =1/4

-1/8 -1/4 -1/2 -1 0 1... =1/8
. . . . . . .
. . . . . . .
. . . . . . =4 <--------rows equal 4

=-2 =-1 =-1/2 =-1/4 =-1/8 =-1/16... -----> =-4 <------------columns equal
-4

yet the table clearly equals 0!

Anyone know why if you add it horizontally, vertically or as a concept that it is different?

SECOND ONE! (GROAN)

If A= infinity, and B= A^A, why is B larger than A?

After all, isn't infinity just that? INFINITY? (no, obviously, or i wouldn't be posting)

To prove it, say a number is larger than another because its SET e.g, 4={1,2,3,4} is larger than another, e.g, 2={1,2}

Infinity's set is {1,2,3,4,5,6,7,8,9,10,11...}.

When it is squared, the numbers increase, e.g 1^1=1, 2^2=4, 3^3=27, etc.

Thus the set becomes: {1,4,27,...}

AND SO INFINITY SQUARED IS LARGER THAN THE INFINITY TO START OFF WITH!!!!!!!1

You're welcome to flame me if you wish.

Last edited by some_random_panda (2006-11-29 20:56:02)

2006-11-29 20:08:33

#2

Superior Mind: (not macbeth); +1,755|7137

math boooooooooo

x

2006-11-29 20:09:42

#3

F0xunseen: Member; +1|7078|Somewhere

I dont get it...

2006-11-29 20:10:17

#4

some_random_panda: Flamesuit essential; +454|6835

Something to do with order of summation... sorry, I do maths as a hobby.

2006-11-29 20:11:13

#5

Fenris_GreyClaw: Real Хорошо; +826|6963|Adelaide, South Australia

some_random_panda wrote:
Infinity.

i get brainaches thinking about that stuff.

2006-11-29 20:13:00

#6

Stags: Member; +26|7100

Don't know you're trying to get to exactly, but every number has an exact opposite in that case.

Also, doing this is an excellent example of Limits. Like the top row horizontally will always go to 2 but never pass it.

2006-11-29 20:30:37

#7

some_random_panda: Flamesuit essential; +454|6835

Stags wrote:
Don't know you're trying to get to exactly, but every number has an exact opposite in that case.

I added the <---- (arrows) to help anyone get their head around it. What i'm trying to say is that if you add numbers up in different ways, you get different results. Yes, Stags, i suppose you're right.

Stags wrote:
Also, doing this is an excellent example of Limits. Like the top row horizontally will always go to 2 but never pass it.

Nicely said.

New one coming up...

2006-11-29 20:35:26

#8

Fenris_GreyClaw: Real Хорошо; +826|6963|Adelaide, South Australia

some_random_panda wrote:
New one coming up...

you make my brain 'splode.

2006-11-29 20:41:04

#9

kr@cker: Bringin' Sexy Back!; +581|6993|Southeastern USA

TAKE THIS EVIL MATH NERD!!!

2006-11-29 20:46:34

#10

Stags: Member; +26|7100

B is bigger than A because B approaches Infinity faster than A. That's the best way I can explain it.

2006-11-29 20:52:40

#11

deepblade_42: Member; +3|6823|N.S.W Australia

I thought you could only use inductive reasoning with real numbers (IE not inf.)

What you're saying holds true for all positive and negative (-2*-2=4 etc) real numbers. Beyond that inductive reasoning falls apart.

BTW 3^3=27 !!!!11!!one!!

2006-11-29 20:55:15

#12

some_random_panda: Flamesuit essential; +454|6835

my bad
+1 for you

Last edited by some_random_panda (2006-11-29 20:55:32)

2006-11-29 20:58:50

#13

Spark: liquid fluoride thorium reactor; +874|7119|Canberra, AUS

In...Inf...Infini....Inifi...I give up.

The paradox is only a conflict between reality and your feeling what reality ought to be.
^{~ Richard Feynman}

2006-11-29 21:02:15

#14

Fenris_GreyClaw: Real Хорошо; +826|6963|Adelaide, South Australia

kr@cker wrote:
TAKE THIS EVIL MATH NERD!!!

W.T.F.

that was the weirdest thing I've ever seen.

2006-11-29 21:05:55

#15

some_random_panda: Flamesuit essential; +454|6835

deepblade_42 wrote:
I thought you could only use inductive reasoning with real numbers (IE not inf.)

What you're saying holds true for all positive and negative (-2*-2=4 etc) real numbers. Beyond that inductive reasoning falls apart.

BTW 3^3=27 !!!!11!!one!!

Well, perhaps my proof for the second one was a little askew, but my first question was correct and the concepts for both puzzles were correct (I learned them from a person who studies this sort of stuff for a living).

Oh yeah, for the first one, the answer is (i think, can't exactly remember), whenever you add infinite positive and negative numbers, the order of summation matters.

2006-11-29 21:08:48

#16

kr@cker: Bringin' Sexy Back!; +581|6993|Southeastern USA

Fenris_GreyClaw wrote:
kr@cker wrote:
TAKE THIS EVIL MATH NERD!!!
W.T.F.

that was the weirdest thing I've ever seen.

sorry, it wasn't meant for you, now you will go to sleep with that ringing in your head and my heart aches for you, i had to pay him back for making me think.

2006-11-29 21:10:37

#17

some_random_panda: Flamesuit essential; +454|6835

kr@cker wrote:
Fenris_GreyClaw wrote:
kr@cker wrote:
TAKE THIS EVIL MATH NERD!!!
W.T.F.

that was the weirdest thing I've ever seen.
sorry, it wasn't meant for you, now you will go to sleep with that ringing in your head and my heart aches for you, i had to pay him back for making me think.

Um...by the way, the link didn't work for me...

2006-11-30 07:36:22

#18

EVieira: Member; +105|6922|Lutenblaag, Molvania

deepblade_42 wrote:
I thought you could only use inductive reasoning with real numbers (IE not inf.)

What you're saying holds true for all positive and negative (-2*-2=4 etc) real numbers. Beyond that inductive reasoning falls apart.

BTW 3^3=27 !!!!11!!one!!

Thats correct. Infinity is not a natural number, nor a set of numbers. Its is a mathematical notation representing an "infinitely" large number, and therefore it behaves differently in such operations.

For example: Infinity + Infinity, Infinity X Infinity both equal Infinity (not 2 Infinity or Infinity square)

Also, remember there there is also -infinity (negative infinity)

Some other examples of how to use infinity in calculations:

Any number divided by infinity = 0. Example 99999999999999 / Infinity = 0

Infinity divided by any number = Infinity. Example Infinity / 99999999999999 = Infinity

Infinity divided by infinity = 1

All of these results can be proven using calculus with limit operations. Swokovsky is a good calculus book, look for it in your library to learn more about infinity and limit operations.

"All truths are easy to understand once they are discovered; the point is to discover them."
Galileo Galilei (1564-1642)

2006-11-30 08:16:27

#19

EVieira: Member; +105|6922|Lutenblaag, Molvania

Link about calculus and limit: http://www.coolmath.com/limit1.htm

"All truths are easy to understand once they are discovered; the point is to discover them."
Galileo Galilei (1564-1642)

2007-06-27 13:23:37

#20

Veridic: Member; +2|6593

some_random_panda wrote:
Say, you have infinite number of columns leading down of infinite numbers in this pattern and infinite rows of infinite numbers leading across in this pattern...

0 1 1/2 1/4 1/8 1/16... =2

-1 0 1 1/2 1/4 1/8... =1

-1/2 -1 0 1 1/2 1/4... =1/2

-1/4 -1/2 -1 0 1 1/2... =1/4

-1/8 -1/4 -1/2 -1 0 1... =1/8
. . . . . . .
. . . . . . .
. . . . . . =4 <--------rows equal 4

=-2 =-1 =-1/2 =-1/4 =-1/8 =-1/16... -----> =-4 <------------columns equal
-4

yet the table clearly equals 0!

Anyone know why if you add it horizontally, vertically or as a concept that it is different?

Okay, It seems to me that most people would assume that a table has square sides. However, in this case, the table would not have square sides.

Example, the second row assumes adding terms to infinity, but it actually contains infinity + 1 terms, with the additional term being the -1 left of the zero. The concept of infinity + 1 does not make sense, but we can think of it as a summation, Σ(1/2^n) from n = 0 to ∞ for the right of the zero (which equals 2), and -1 for the left of the zero.

If the table did have square sides, the very last term in the summation of the second row would be omitted: Σ(1/2^n) from n = 0 to (∞-1). This is how the error is generated.

You are correct that finite table would equal zero, however an infinite table is not possible as you have made it, since it cannot be square.

2007-06-28 02:25:55

#21

PureFodder: Member; +225|6729

people seem to be forgetting that any maths that begins with something like 'add up all the numbers to infinity' is begining with a step that can't be completed.

In the examples of A= infinity and B=A^A as A is an abstract concept itself that cannot ever be reached then this fails as a maths problem at step one. A dosn't equal infinity, A heads off towards infinity and is a term that can not be mathematically completed.

2007-06-28 02:32:23

#22

SharkyMcshark: I'll take two; +132|7229|Perth, Western Australia

some_random_panda wrote:
SECOND ONE! (GROAN)

If A= infinity, and B= A^A, why is B larger than A?

After all, isn't infinity just that? INFINITY? (no, obviously, or i wouldn't be posting)

To prove it, say a number is larger than another because its SET e.g, 4={1,2,3,4} is larger than another, e.g, 2={1,2}

Infinity's set is {1,2,3,4,5,6,7,8,9,10,11...}.

When it is squared, the numbers increase, e.g 1^1=1, 2^2=4, 3^3=27, etc.

Thus the set becomes: {1,4,27,...}

AND SO INFINITY SQUARED IS LARGER THAN THE INFINITY TO START OFF WITH!!!!!!!1

You're welcome to flame me if you wish, but Karma would be appreciated more as i have a lack of it.

Oh hello. You're missing something. The concept of infinity implies a never ending set. So starting with {0, 1, 2, 3, 4...} going to {0, 1, 4, 9, 16...}, all of those numbers are a subset of infinity. A tough concept to wrap ones head around I know.

2007-06-28 02:40:04

#23

pirana6: Go Cougs!; +697|6735|Washington St.

I can't explain the first one but I can give you an answer for the second one (if it hasn't been posted yet, I didn't want to read all that):

Infinity is not a number, it is a concept (theory), therefore you cannot treat it like a number. You cannot add, multiply, subtract or divide by, to, from or with infinity. 1/∞ although would LIMIT at zero you can't actually use it in non-conceptual math, meaning, you can only use it to visualize something like limits but you can't actually perform any actions with it.

Last edited by pirana6 (2007-06-28 02:40:48)

2007-06-28 02:49:25

#24

NemeSiS-Factor: Favorite Weapon? Pistol; +29|7114|Everett, WA, US

some_random_panda wrote:
I thought that this was interesting and so i removed it from the post and put it in this one...

Say, you have infinite number of columns leading down of infinite numbers in this pattern and infinite rows of infinite numbers leading across in this pattern...

0 1 1/2 1/4 1/8 1/16... =2

-1 0 1 1/2 1/4 1/8... =1

-1/2 -1 0 1 1/2 1/4... =1/2

-1/4 -1/2 -1 0 1 1/2... =1/4

-1/8 -1/4 -1/2 -1 0 1... =1/8
. . . . . . .
. . . . . . .
. . . . . . =4 <--------rows equal 4

=-2 =-1 =-1/2 =-1/4 =-1/8 =-1/16... -----> =-4 <------------columns equal
-4

yet the table clearly equals 0!

Anyone know why if you add it horizontally, vertically or as a concept that it is different?

SECOND ONE! (GROAN)

If A= infinity, and B= A^A, why is B larger than A?

After all, isn't infinity just that? INFINITY? (no, obviously, or i wouldn't be posting)

To prove it, say a number is larger than another because its SET e.g, 4={1,2,3,4} is larger than another, e.g, 2={1,2}

Infinity's set is {1,2,3,4,5,6,7,8,9,10,11...}.

When it is squared, the numbers increase, e.g 1^1=1, 2^2=4, 3^3=27, etc.

Thus the set becomes: {1,4,27,...}

AND SO INFINITY SQUARED IS LARGER THAN THE INFINITY TO START OFF WITH!!!!!!!1

You're welcome to flame me if you wish.

I don't understand the pattern. From the top down your going 1, 0, -1, -1/2, -1/4? How is that a pattern? The -1 seems very much out of place in there.

2007-06-28 03:05:19

#25

=OBS= EstebanRey: Member; +256|6994|Oxford, England, UK, EU, Earth

i'm quite good at maths and I can't understand one word of this...

BF2S Forums Infinity

some_random_panda wrote:

Stags wrote:

Stags wrote:

some_random_panda wrote:

kr@cker wrote:

deepblade_42 wrote:

Fenris_GreyClaw wrote:

kr@cker wrote:

kr@cker wrote:

Fenris_GreyClaw wrote:

kr@cker wrote:

deepblade_42 wrote:

some_random_panda wrote:

some_random_panda wrote:

some_random_panda wrote:

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