.9999999 repeating forever = 1

[Duckenheimer]

Or the number is constantly changing

*grabs popcorn*

[AJ010]

Or the number is constantly changing

There is no "constantly changing" number. A number is a number, lol.

lol I just saw your edit. what are you talking about? Numbers are figures

[Klippymitch]

There is no "constantly changing" number. A number is a number, lol.

Why can't numbers be relative to each other?

Every growth to an infinite number is the same growth of the finite number. Numbers are still the same value relative to each other but yet value is different in other relative view point.

[MHG3]

There is no "constantly changing" number. A number is a number, lol.

Yes there is "i"

[Duckenheimer]

Why can't numbers be relative to each other?

They are relative to each other, in a fixed manner. That's the whole basis of mathematics as a system that works the same today as it does tomorrow.

If a number of some amount changes for whatever purpose, it is represented with different notation.

Why can't numbers be relative to each other?

Every growth to an infinite number is the same growth of the finite number. Numbers are still the same value relative to each other but yet value is different in other relative view point.

Remember .33... has an infinite amount of digits in representing what it does, which happens to be a FINITE number/amount.

Every single finite number can be represented in the decimal system with an infinite amount of digits. That does not change the fact that the actual amount is and remains finite. Some finite numbers cannot be represented with a finite number of digits.

[AJ010]

Yes there is "i"

meh I mean real numbers lol

[BrettT07]

lol horrible

How so?

[MHG3]

meh I mean real numbers lol

Just keeping you honest

[secondhandloser]

1/3rd of something, or 1 of something, is not an infinite amount of something.

Surely you will agree that 0.999... is smaller than 1.1!!!

Yet 1.1 is a smaller amount than infinity!!! How could this be?!?!

CLUE: The representation uses an infinite amount of digits. This does not mean the amount being represented BY the digits is actually an infinite amount. (ie 0.333... apples is not an infinite amount of apples. It's not even half of one..., how could it be an infinite amount?)

You have proven my point very well.

People still want to say that every mathematician in the world, maths itself, and the decimal system are all wrong but they are right, because they don't like/understand how the decimal system works as a numerical way of representing real amounts.

No ****. Strong failure on the reading comprehension. It is an infinitely repeating number.

[AJ010]

Just keeping you honest

to be more honest, I haven't studied much abstract math with imaginary numbers. ive mostly dealt with the real numbers. do you know any sites I could check out to learn more about them?

[Duckenheimer]

No ****. Strong failure on the reading comprehension. It is an infinitely repeating number.

I know it is a number of infinitely repeating digits that represents the amount.

The AMOUNT of something actually being represented, on the other hand, is FINITE, like I proved.

What I said:

"People are getting confused because they are thinking the amount being represented is actually infinite"

What you said:

"That's because it it."

No it isn't. The digits used are infinite. The amount being represented isn't, like I just proved. Strong failure on reading comprehension indeed.

STRONG denial in this thread. Fascinating psychologically though.

[secondhandloser]

Yes there is "i"

As in V/R = I

...oh, sorry.

[MHG3]

Huh? i is a perfectly defined constant in R^2=C.

i = square root of -1

[secondhandloser]

I know it is a number of infinitely repeating digits that represents the amount.

The AMOUNT being represented, on the other hand, is FINITE, like I proved.

What I said:

"People are getting confused because they are thinking the amount being represented is actually infinite"

"That's because it it."

No it isn't. The digits used are infinite. The amount being represented isn't, like I just proved. Strong failure on reading comprehension indeed.

STRONG denial in this thread. Fascinating psychologically though.

Except I agreed with you. Kinda funny how bad your reading is.

[MiscMathematician]

to be more honest, I haven't studied much abstract math with imaginary numbers. ive mostly dealt with the real numbers. do you know any sites I could check out to learn more about them?

My professor wrote a great book on Real Analysis that also deals with multivariable/complex analysis: http://www.math.binghamton.edu/denni...f07/EleAna.pdf

[AJ010]

i = square root of -1

What I don't get is, how is "i" a constantly changing number?

i = sqrt(-1)
2i = sqrt (-4)

Every number in the reals stand for one thing. 1 = 1, 2 = 2, etc. So, how does i represent different things?

[MiscMathematician]

i = square root of -1

Which is a constant. (0,1) in R^2 = sqrt(-1) in C.

[AJ010]

My professor wrote a great book on Real Analysis that also deals with multivariable/complex analysis: http://www.math.binghamton.edu/denni...f07/EleAna.pdf

Thanks !

[Duckenheimer]

Except I agreed with you. Kinda funny how bad your reading is.

"People are getting confused because they are thinking the amount being represented is actually infinite"

"That's because it it."

It seems like you are saying "that's because it is" (I assume you meant "is"), ie. saying the amount being represented is actually infinite.

I do not understand how my reading is at fault here, because you seem to be disagreeing, and I cannot comprehend reading this in a way in which you are agreeing with my statement. Care to clarify?

[MiscMathematician]

Thanks !

NP. After you finish that, take a look at Walter Rudin's Principles of Mathematical Analysis. It's an entry-level grad / advanced undergrad text covering nearly everything you need to know about late Analysis. Next step would be Functional Analysis (also by Rudin) which is the holy grail of Analysis books. Haven't touched it yet, but I'm planning on it shortly.

[chenbot]

hai guys I just bought a 1 pound pie for me and 2 of my buds. I want to divide it exactly equally between the three of us with my new found computer-aided laser guide pie cutter to cut perfectly accurately, atomic weight scale to make sure that the slices are equal, and electron microscope to make sure no crumbs are lost. However, I have recently been informed by Klippymitch and Pad that regardless of how hard I try, it is impossible to divide the pie into thirds, because there is no such thing in the real world as 1/3 of 1! What am I supposed to do?!

[MiscMathematician]

hai guys I just bought a 1 pound pie for me and 2 of my buds. I want to divide it exactly equally between the three of us with my new found computer-aided laser guide pie cutter to cut perfectly accurately, atomic weight scale to make sure that the slices are equal, and electron microscope to make sure no crumbs are lost. However, I have recently been informed by Klippymitch and Pad that regardless of how hard I try, it is impossible to divide the pie into thirds, because there is no such thing in the real world as 1/3 of 1! What am I supposed to do?!

The number of atoms of each ingredient would have to be divisible by three. Atoms are technically discrete in quantity.

[PunkGoesSwoll]

1.99999999999..... = 2

[Duckenheimer]

hai guys I just bought a 1 pound pie for me and 2 of my buds. I want to divide it exactly equally between the three of us with my new found computer-aided laser guide pie cutter to cut perfectly accurately, atomic weight scale to make sure that the slices are equal, and electron microscope to make sure no crumbs are lost. However, I have recently been informed by Klippymitch and Pad that regardless of how hard I try, it is impossible to divide the pie into thirds, because there is no such thing in the real world as 1/3 of 1! What am I supposed to do?!

DON'T try and divide it into exact thirds. You will explode the universe!!!

1.99999999999..... = 2

**** just got real.

[Pad264]

0.333... is a finite number. If the pie is cut in 3 pieces of EXACTLY the same size (down to the smallest molecule) it could only possibly be represented in decimal form as 0.333... as a proportion of the pie.

The exact amount of molecules on the other hand, in the pie, can be represented without denoting an infinite amount of decimal places. (and also represented WITH denoting them too, as with any real number).

So lets say there's exactly 1 billion molecules in each slice. That's concrete and finite. And each of them are EXACTLY 33.333....% of the whole pie.

Remember the decimal system is just a system of representing amounts. No infinite amount is being represented here, the only infinity is the amount of digits used in notation.



What exception am I making?

.33... = 1/3

.99... = 3/3

The point is that you cannot divide the pizza into precisely three EQUAL parts. Even if you have to take the decimal 50 trillion places out, it will eventually become a finite number. We're not talking about math, we're talking about physics. The laws of the universe do not allow us to divide any object as precisely as you can in a math formula.

You are defending the ".99 repeating" is equal to 1 equation on the basis of a mathematical fact. We're not talking about math...your defense for the equation cannot be, "It is fact because it is fact," once we're no longer having a mathematical discussion. The laws of math do not apply outside the world of math. It is no different than any other language. A window is a "window"...but in Italy, it's a "finestra." The "laws" change. The fact that Math is universally accepted by all cultures, as opposed to written/spoken languages, does not mean that it applies to all of the universe.

Theoretical math allows us to be more precise than we can ever hope to be in practice. Even with technology exponentially improving, we can never hope to achieve an infinite measurement in the world.

[old_Mark_NW]

We gonna hit 500 posts on this subject?

WA-HOO !!!

[Pad264]

People are getting confused because they are thinking the amount being represented is actually infinite in some way.

Again, you are distinguishing between ".99 repeating" and any other repeating number. Is ".33 repeating" not infinite? How about ".44 repeating"? You are making an exception for ".99 repeating" based soley on a mathematical proof that does not apply to anything other than math.

Read that last sentence again...because it's tough to imagine a world without math. Math is everywhere. What you must understand is that math is not inherent to the universe, it was applied to the universe.

[M@XLOL]

[Pad264]

All repeating decimals are rational numbers. It hust HAPPENS that 0.999... is the rational number 1/1=2/2=3/3=....

All rationals can also be represented by infinitely repeating decimals, e.g. 3.4 = 3.40000...

Consider this: ANY rational number of the form k.abcabcabcabc... (where abc is repeating, a b and c are positive integral digits in base 10 and k is any integer) is simply the rational number (999*k+abc)/999. For abcd, divide and multiply by 9999, etc. For an arbitrary base, say base B, use (B-1) istead of 9.

I think I may have understood what you said, but I'm not sure what the point was.

(Note: It is also possible that I did not understand what you said.)

[Duckenheimer]

Again, you are distinguishing between ".99 repeating" and any other repeating number. Is ".33 repeating" not infinite? How about ".44 repeating"? You are making an exception for ".99 repeating" based soley on a mathematical proof that does not apply to anything other than math.

Read that last sentence again...because it's tough to imagine a world without math. Math is everywhere. What you must understand is that math is not inherent to the universe, it was applied to the universe.

The digits used in representation are infinite, the amounts being represented are clearly NOT.

What exception am I making for .99...? (ie 1?)