Does point 999 repeating equal 1?

[ToriAllen]

We were talking about asymptotes in math class the other day, and half the class could not understand for the love of god that the line on the graph would NEVER touch the asymptote, it would infinitely get closer, but never touch.

 

That's the same principle as 0.9999 will never actually equal one. It can get infinitely closer, but it will never touch. It will never be.

 

0.99999999999999999999999999999999 not equal to 1.

 

They even look different

Just curious, but did they present this as an opinion, or as something that's cold hard fact?

Not quite the same principle. It was an interesting fact he was showing us along with the explanations of why.

Here you go:

 

1/3 = .33333333 to infinity

2/3 = .66666666 to infinity

 

.3333333 to infinity + .6666666 to infinity = .9999999 to infinity

But

1/3 + 2/3 = 3/3 = 1

 

Therefore .9999999 to infinity = 1

 

That is my math lesson for today.

[Mohammed_Rots_In_Hell]

Not quite the same principle. It was an interesting fact he was showing us along with the explanations of why.

Here you go:

 

1/3 = .33333333 to infinity

2/3 = .66666666 to infinity

 

.3333333 to infinity + .6666666 to infinity = .9999999 to infinity

But

1/3 + 2/3 = 3/3 = 1

 

Therefore .9999999 to infinity = 1

 

That is my math lesson for today.

Very nice, Tori! Looks good to me as long as addition is defined for repeating decimals... I'm not sure about it. However if it is, then look at the follwing addition:

 

If addition for repeating decimals is defined then:

.999(repeating) + .111(repeating) equals 1.111(repeating) because each digit would have a significant digit (one) added to it and 9 and 1 leaving 11 and you would carry that one to the next 9 and 1 (from infinity).

 

set A = .999(repeating), B = .111(repeating)

A + B = 1.111(repeating)

A + B = 1 + .111(repeating)

 

subtract B from both sides

A = 1

 

 

 

What do you think?

[Mohammed_Rots_In_Hell]

Ok, I smoked a fat joint the other night and went over this. I had to go to the ER assclown! lol Thanks alot.

Just be glad I didn't recommend any LSD!

[TheJenn88]

Not quite the same principle. It was an interesting fact he was showing us along with the explanations of why.

Here you go:

 

1/3 = .33333333 to infinity

2/3 = .66666666 to infinity

 

.3333333 to infinity + .6666666 to infinity = .9999999 to infinity

But

1/3 + 2/3 = 3/3 = 1

 

Therefore .9999999 to infinity = 1

 

That is my math lesson for today.

 

Thank you! I get it now..don't know if I quite "agree" (but who am I to even decide? Like I can even add 5+5). Made a lot more sense than MRIH

[Mohammed_Rots_In_Hell]

Thank you! I get it now..don't know if I quite "agree" (but who am I to even decide? Like I can even add 5+5). Made a lot more sense than MRIH

Is this an indictment against my powers of persuasion, or against your powers of comprehension?

[Mohammed_Rots_In_Hell]

This is basically the same proof that Tori gave...

 

1/3 = .333(repeating)

 

1/3 3 = 1

.333(repeating) 3 = .999

 

1 = .999(repeating)

[EnterNetProphet]

For a better explanation, CLICK HERE .

.

.

 

Gee thanks..I needed the reboot

 

 

clicks----->"Don't send error report to micro$oft" :o

[ToriAllen]

This is basically the same proof that Tori gave...

 

1/3 = .333(repeating)

 

1/3 3 = 1

.333(repeating) 3 = .999

 

1 = .999(repeating)

Thief!!...basically.

[ToriAllen]

Like I can even add 5+5.

I believe that is 10...

Your welcome.

[Mohammed_Rots_In_Hell]

Thief!!...basically.

Yes, I am! (A thief)... The best proof I know of is the one I posted about lines. For any two distinct points on a line, there must exist at least one point in between them. (Actually, it has been prooven that for any two points on a line there must exist an infinite number of points between them). There is no point between .999(repeating) and 1.

 

You may argue that .999(repeating) is not a rational number, but even if that is true, irrational numbers occupy a point on a line (just look at pi, the square root of 2, or e from natural logrithms).

 

Georg Cantor attempted to explain Zeno's first paradox with the set of all halves.

 

Zeno was a Greek philosopher who lived in Plato's time. Zeno came up with the 4 paradoxes of motion. The first paradox states that for any object to traverse two points (A & B), the object must first pass through the mid-point of those two points (B'), and before it can reach the midpoint of the initial two (B'), it must first reach the midpoint(B'') of the first point(A) and the initial midpoint(B), and before it can reach the midpoint of A - B'' it must reach the midpoint(B''') of A - B'', this concievably goes on fo ever, so the object can never get started.

 

Georg Cantor suggested that the equation could be represented as a sumation of the set of all haves, that is 1/2 + 1/4 + 1/8 + 1/16 + ... + 1/(2 ^ infinity) = 1. He then prooved this correct

 

So I was wondering if the same proof could be used (the set of all 9/10ths) to prove it. 9/10 + 9/100 + 9/1000 + ... 9/(10 ^ infinity) = 1 ???

 

just a thought.

[ToriAllen]

You may argue that .999(repeating) is not a rational number, but even if that is true, irrational numbers occupy a point on a line (just look at pi, the square root of 2, or e from natural logrithms).

.9999 repeating is a rational number. Irrational numbers go into infinity without repeating or having a pattern of any kind. Just thought I would clear up that little point.

.123123123123 repeating = rational

.846795456756176535787 none repeating = irrational

[TheJenn88]

Is this an indictment against my powers of persuasion, or against your powers of comprehension?

 

Well, considering I have the qualifications of a grade 10 math student, I'd have to say mostly comprehension. Since I'm not versed in math jargon, Tori did a better job explaining.

[TheJenn88]

I believe that is 10...

Your welcome.

 

Thanks. You saved me from failing my math test

[Mohammed_Rots_In_Hell]

.9999 repeating is a rational number. Irrational numbers go into infinity without repeating or having a pattern of any kind. Just thought I would clear up that little point.

.123123123123 repeating = rational

.846795456756176535787 none repeating = irrational

I know it is a rational number because it is the same as 1, and of course one is a rational number

[builder]

I know it is a rational number because it is the same as 1, and of course one is a rational number

 

Agreed.

 

In fact, the only irrational thing about this whole scenario is..............,

 

how come this "debate" has gone on for so many pages?

 

Perhaps 9 repeating can equal 1. Who really gives a flying fuck anyway? Huh?

[Mohammed_Rots_In_Hell]

Perhaps 9 repeating can equal 1. Who really gives a flying fuck anyway? Huh?

Those with IQ's greater than 90. Intelectual debate by Plato, Socrates, Aristotle, etc. etc. is the foundation of all of your creature comforts that you enjoy today. Without Pythagoris or Euclid you'd have to walk to work to the local quarry and bust rocks, because that would be the best technology around. You can show off your stupidity if you want, but if you don't like intelectual debate then go read something else like the piss pot, playboy, sports illustrated, or Dr. Seuss

[builder]

Those with IQ's greater than 90. Intelectual debate by Plato, Socrates, Aristotle, etc. etc. is the foundation of all of your creature comforts that you enjoy today. Without Pythagoris or Euclid you'd have to walk to work to the local quarry and bust rocks, because that would be the best technology around. You can show off your stupidity if you want, but if you don't like intelectual debate then go read something else like the piss pot, playboy, sports illustrated, or Dr. Seuss

 

And a big Fuck You to you too.

 

I enjoy mathematics. I use one theory of Pythagoris on a weekly basis. 3-4-5 ring any bells?

 

If you want to discuss mathematical probabilities, why are you talking base numbers? Or are you more comfortable with such inane bullshit as one third?

 

Discuss Pi.

 

Challenge yourself, for a change.

[Mohammed_Rots_In_Hell]

And a big Fuck You to you too.

The only inteligent thing in this entire post... How did you manage, builder?

 

I enjoy mathematics.

I'm sure you do.

 

I use one theory of Pythagoris on a weekly basis.

lol

 

3-4-5 ring any bells?

reference to a right triangle with the sides measuring 3 and 4 and the hypoteneuse measuring 5? If so, then what are the angles?

 

If you want to discuss mathematical probabilities, why are you talking base numbers?

1) I never mentioned probabilities, but it it is one of my specialities. I was going to take the actuary exam... but, alas, I am a lowly software engineer.

2) I use base ten as a default when talking about numbers, binary, hex and octal for some of my work. What the fuck, builder? What "base" of number do want to talk about? I hope it makes sense (but I somehow doubt it)

 

Or are you more comfortable with such inane bullshit as one third?

Yeah 1/3 is cool BTW, if you want a chalenge, do you know what the "cantor set" is? it is based an one third of a line segment, it is very interesting.

 

Discuss Pi.

Normally, the orginator of a subject traditionally will kick of the discussion, but since you obviously have nothing to contribute, I'll start with Archemedies. Archemedies was probably the greatest mathematician of all time until builder the white trash Australian. Archemedies developed the scientific method for calculating Pi. Start with 22/7 < Pi < 223/71, next you use the formula Pi = 12 arctan(3 ^ (1/2) - 2); then you start approximating the value of 3 ^ (1/2)... that will give Pi to the significance you calculate the square root of 3.

 

Challenge yourself, for a change.

Good point, I think I'll have another bong hit!

[Cogito Ergo Sum]

Hmmm...

 

Put's on Professor's Cap along with reading glasses on the end of nose

 

This is far easier than some try to make it.

 

To establish a credible proving or disproving, let us look at each of the numbers in relationship to their substitution in complimentary functions. If in fact .999 = 1, then all relustant values of the functions will remain the same as well because as we know, 1 = 1.

 

For Example:

 

If we look at the respective functions of

 

.999tan(x)=0 [-10;10]

 

versus

 

1tan(x)=0 [-10; 10]

 

and graph these respective functions, they will INITIALLY look identical until we begin to plot points along the graph.

 

Note: Curiously though, the Number of roots found in each equation is: 7

 

x1 -9.42477796

x2 -6.28318531

x3 -3.14159265

x4 0

x5 3.14159265

x6 6.28318531

x7 9.42477796

 

So, let us look closer through the use of ancillary functions.

 

Let's for example, examine the VALUES of the following for x:

 

f(x)

and f '(x) [f prime of x]

 

Assuming x = -10.19435692 in both equations -

 

The results are different!

 

1tan(x)=0 [for f(x)] will equal -0.96885173

 

while

 

.999tan(x)=0 [for f(x)] will equal -0.9688288

 

AND

 

1tan(x)=0 [for f '(x)] will equal 1.93867368

 

while

 

.999tan(x)=0 [for f '(x)] will equal 1.936735.

 

Furthermore, as the value of x either increases above 10, or decreases below -10, continuing on respectively to either positive or negative infinity, the discrepency for the values of f '(x) will become clearly evident.

 

Thus, the concept that .999 = 1 does not withstand strict mathematical scrutiny in relation to substitution within f(x) nor f '(x) within the given functions.

 

This also works for other functions like tan(.999x)=0 and tan(1x)=0 or any other function you want to choose.

 

Okay, how about something interesting now....like perfect tits

[builder]

Builder in Blue:

The only inteligent thing in this entire post... How did you manage, builder?

I consult my psychic, and monitor the position of the moon.

 

I'm sure you do.

 

It's worth it. She has great tits.

 

lol

 

Oh yeah. Still pointing up, too.

 

reference to a right triangle with the sides measuring 3 and 4 and the hypoteneuse measuring 5? If so, then what are the angles?

 

Sixty and thirty. Duh.

 

1) I never mentioned probabilities, but it it is one of my specialities. I was going to take the actuary exam... but, alas, I am a lowly software engineer.

2) I use base ten as a default when talking about numbers, binary, hex and octal for some of my work. What the fuck, builder? What "base" of number do want to talk about? I hope it makes sense (but I somehow doubt it)

 

Yeah 1/3 is cool BTW, if you want a chalenge, do you know what the "cantor set" is? it is based an one third of a line segment, it is very interesting.

 

Normally, the orginator of a subject traditionally will kick of the discussion, but since you obviously have nothing to contribute, I'll start with Archemedies. Archemedies was probably the greatest mathematician of all time until builder the white trash Australian. Archemedies developed the scientific method for calculating Pi. Start with 22/7 < Pi < 223/71, next you use the formula Pi = 12 arctan(3 ^ (1/2) - 2); then you start approximating the value of 3 ^ (1/2)... that will give Pi to the significance you calculate the square root of 3.

 

Good point, I think I'll have another bong hit!

 

You are so kind to mention me in that rant.

 

I have recorded it for posterity.

 

Thankyou.

 

Fuckin arsewipes, genuflecting heathens.

[Mohammed_Rots_In_Hell]

Hmmm...

 

Put's on Professor's Cap along with reading glasses on the end of nose

 

This is far easier than some try to make it.

You look mighty purdy!

 

To establish a credible proving or disproving, let us look at each of the numbers in relationship to their usage in complimentary functions.

 

For Example:

 

If we look at the respective functions of

 

.999tan(x)=0 [-10;10]

 

versus

 

1tan(x)=0 [-10; 10]

Ok, just to clarify... we are looking at

 

.999(repeating) tan(x) = y for all values between 10 and negative 10... right? -AND-

 

1 tan(x) = y for the same values????

 

-OR DO YOU MEAN-

 

.999(repeating) tan(x) = 0

1 tan(x) = 0

 

then x would be 0 in any case regardless (since the tangent of 0 is 0)

 

 

and graph these respective functions, they will INITIALLY look identical until we begin to plot points along the graph.

 

Note: Curiously though, the Number of roots found in each equation is: 7

 

x1 -9.42477796

x2 -6.28318531

x3 -3.14159265

x4 0

x5 3.14159265

x6 6.28318531

x7 9.42477796

CES, There are an infinit number of points on any graph of a function with at least two points. I am not sure what you mean by "roots" here... Do you mean possible values for y? because they are infinite...

 

The results you have here look more like the results of

 

x = Pi(y) for all integers between 3 and -3.

 

 

So, let us look closer through the use of ancillary functions.

 

Let's for example, examine the VALUES of the following for x:

 

f(x)

and f '(x) [f prime of x]

the derivative on tan(x) is 1/tan(x)... what do you mean by f'(x) ?????

 

Oh well, let's carry on...

 

Assuming x = -10.19435692 in both equations -

 

The results are different!

 

1tan(x)=0 [for f(x)] will equal -0.96885173

 

while

 

.999tan(x)=0 [for f(x)] will equal -0.9688288

 

AND

 

1tan(x)=0 [for f '(x)] will equal 1.93867368

 

while

 

.999tan(x)=0 [for f '(x)] will equal 1.936735.

 

the tangent of (-10.19435692) = -0.968851734144359 true.

and if you multiply it by .999 you get -0.967882882410215

 

 

and for f'(x) we get -1.03214967239869 not 1.93867368

and multiplied by .999 we get -1.03318285525394 not 1.936735

 

-BUT-

 

We are talking about .999(repeating) --- key word , the 9's repeat forever! not just three of them!

[builder]

And what a rivettiing tale of drama we have here. Just how many nines can you squeeze into 1.

 

I'm shopping for shares in this ground-breaking research enterprise.

 

It''s gonna be big.

[Mohammed_Rots_In_Hell]

And what a rivettiing tale of drama we have here. Just how many nines can you squeeze into 1.

The answer is (if you have been reading and comprehending) is All of them

 

I'm shopping for shares in this ground-breaking research enterprise.

You do that.

 

It''s gonna be big.

whatever

[Mohammed_Rots_In_Hell]

reference to a right triangle with the sides measuring 3 and 4 and the hypoteneuse measuring 5? If so, then what are the angles?

 

Sixty and thirty. Duh.

You make me laugh, Einstein! here is the formula for you:

cos(x) = 4/5 ; x is the small angle

cos(x) = 3/5 ; x is the large angle

 

solve for x, genius

 

DUH!

[builder]

You make me laugh, Einstein! here is the formula for you:

cos(x) = 4/5 ; x is the small angle

cos(x) = 3/5 ; x is the large angle

 

solve for x, genius

 

DUH!

 

And you've just demonstrated the difference between practical reality, and possessive ideology.

 

I use maths for profit. You abuse it for perverse entertainment.