1 = ?

[Dark]

Take a whole cirlce, it's counted as being a whole, so it's 1.

 

Now divide it by 3, so you get 3 pieces of the circle, 33.33333...

 

I don't understand how 1 divided by 3 gets you 33 and three repeating. Unless I forgot to divide by zero and multiply by pi. That might be the problem.

 

Someone probably already showed this, but I'm not sure.

 

x = .999...

10x = 9.999...

 

Subtract the second equation by the first.

 

9x = 9

x = 1

 

So, 1 = .999...

 

I could attempt to prove that 0.000...1 is equal to 0, but Crab will probably come here and whip me with a fish for getting it wrong.

[CrabHelmet]

I could attempt to prove that 0.000...1 is equal to 0' date=' but Crab will probably come here and whip me with a fish for getting it wrong.

[/quote']

 

I'd say such an endeavour would be failed from the outset, as you would first need a meaningful definition of 0.000...1.

[Dark]

I could attempt to prove that 0.000...1 is equal to 0' date=' but Crab will probably come here and whip me with a fish for getting it wrong.

[/quote']

 

I'd say such an endeavour would be failed from the outset, as you would first need a meaningful definition of 0.000...1.

 

Ahh, this oughta be a toughy.

 

My original definition was 'a number that can be added to .999... to attain a sum of 1'.

 

But since we have proven that .999... = 1, that is automatically proven as 0.

 

Not really a mathematical definition, but 'a number with zeroes such that the one is in the lowest place value of the decimal system'.

[CrabHelmet]

I could attempt to prove that 0.000...1 is equal to 0' date=' but Crab will probably come here and whip me with a fish for getting it wrong.

[/quote']

 

I'd say such an endeavour would be failed from the outset, as you would first need a meaningful definition of 0.000...1.

 

Ahh, this oughta be a toughy.

 

My original definition was 'a number that can be added to .999... to attain a sum of 1'.

 

But since we have proven that .999... = 1, that is automatically proven as 0.

 

Not really a mathematical definition, but 'a number with zeroes such that the one is in the lowest place value of the decimal system'.

 

But the decimal system has no lowest place value. It has the same Von Neumann order-type as the positive integers, which means that you can find a last decimal place only in the sense that you can find a last positive integer (i.e. you can't).

[Azmodius]

all of math is stupid

 

Normaly, I would provide a rebbutal on how it is very usefull, but not this time.

 

BEST POST EVAR.

[Reaper of Shadows]

limit theory disproves that

[CrabHelmet]

Calculus was originally developed at least by one of its inventors purely for the purposes of conducting siege warfare - it was necessary to calculate the proper way to attack with trebuchets and hit the intended target.

[Yogg-Saron]

That's the reason the 3s repeat.

 

Just because your calculator stopped doesn't mean the number has stopped.

 

:3

[Reaper of Shadows]

thatz the problem

releying on the calcs information

[Womi]

00000001 + 00000001 = 00000010

 

It's true' date=' no joke.

[/quote']

 

A byte is so much cooler. <_<

[Scatty]

I will prove all of you wrong!

 

 

Take A. A is the value of an Ace is the game of Blackjack.

 

According to the rules,

 

A=1

 

But, according to the same rules,

 

A=11

 

So, using simple logic, we would have

 

1=11

 

Right?

 

(the above statement is a joke made up for the sake of post count)

[Womi]

No.

Owait, this was a joke?

[Scatty]

Yup. POST COUNT POWAH!

[Raylen]

Guys.

 

Let's assume some number x = 0.9 repeated.

 

So: 10 x = 9.9 repeated

 

10 x - x = 9.9 repeated - 0.9 repeated

 

9x = 9

 

x = 1.

 

This method can be used to evaluate any form of repeating fraction.

 

I.e. 0.17 repeated

 

x = 0.17 repeated

 

100 x = 17.17 repeated.

 

100 x - x = 17.17 repeated - 0.17 repeated

 

99x = 17

 

x = 17/99

 

What's going on is that you guys haven't defined the equal sign correctly. In formal logic, the definition of equals is that there are no numbers between the LS and RS.

[Scatty]

No REAL NUMBERS, for that matter.

[gizmo00999]

Doesn't this have to do something with Pi? :) or PI or however u wanna call it (the little greek letter)

[Womi]

Except being infinite....No. Not really. =)

[Dark]

Calculus was originally developed at least by one of its inventors purely for the purposes of conducting siege warfare - it was necessary to calculate the proper way to attack with trebuchets and hit the intended target.

 

Didn't Newton invent calculus to provide a mathematical proof that planets orbit in ellipses?

 

Guys.

 

Let's assume some number x = 0.9 repeated.

 

So: 10 x = 9.9 repeated

 

10 x - x = 9.9 repeated - 0.9 repeated

 

9x = 9

 

x = 1.

 

This method can be used to evaluate any form of repeating fraction.

 

I.e. 0.17 repeated

 

x = 0.17 repeated

 

100 x = 17.17 repeated.

 

100 x - x = 17.17 repeated - 0.17 repeated

 

99x = 17

 

x = 17/99

 

What's going on is that you guys haven't defined the equal sign correctly. In formal logic' date=' the definition of equals is that there are no numbers between the LS and RS.

[/quote']

 

A tad late.

[CrabHelmet]

What's going on is that you guys haven't defined the equal sign correctly. In formal logic' date=' the definition of equals is that there are no numbers between the LS and RS.

[/quote']

 

That's an extremely narrow definition that breaks down horribly when you're dealing with most things that aren't the set of real numbers, since it relies on the existence and definition of a specific total ordering that not only is not a well-ordering but also has other required properties related to density and such. A better definition is that two objects are equal if they represent the same element.

[Raylen]

@ Crab: I completely agree with you. But I'm still learning, density theorem is best thing I know. :).

[Scatty]

@ Crab: Haven't you just said the same think twice?

[CrabHelmet]

@ Crab: I completely agree with you. But I'm still learning' date=' density theorem is best thing I know. :).

[/quote']

 

Density works decently for its purposes; it's just that its purposes don't generalize beyond R terribly well. It still seems most reasonable to me to use the "two objects are equal if they are the same element" definition and then just use density to prove that those two objects are indeed the same element.

 

@ Crab: Haven't you just said the same think twice?

 

You will have to be more specific as to what same thing that is that you suppose I have said twice.

[Shrekstasy]

Divide by 0

[Scatty]

@You said two objects are equal if they represent the same thing. And that's very redundant, if you ask me.

@Twisted: Infinity. Or negative infinity, depends on the situation.

[CrabHelmet]

@You said two objects are equal if they represent the same thing. And that's very redundant' date=' if you ask me.

[/quote']

 

We're defining equality. If you already have a definition of equality in mind, then stating that definition will come across as a tautology. However, until you have defined equality, the "=" sign is completely meaningless, and thus a definition is required.

 

The definition of equality varies significantly depending on your system and objectives. For example, two cardinalities are equal if the sets to which they correspond are bijective. Equality must be defined to have meaning, even if that definition is intuitive.

 

@Twisted: Infinity. Or negative infinity' date=' depends on the situation.

[/quote']

 

No.

 

I have no desire to go into detail here, but you are wrong.