A question of numbers (one for the maths fans)

As I said, its a question of defintions and number systems. In base ten, if you multiply by 10 the decimal point moves. Actually, in any base if multpily by 10 the decimal point moves, in base ten 10 means ten. It's an integral part of what the number 10 is.In 0.999 we don't lose the 9/1000. All that happens is that the 1000ths column becomes 0 because the digits are shifted up one column (in base 10). when there are an infinite number of 9s we don't put a zero at the end, but the essential operation (shifting the digits up a column) can still happen. This is part and parcel of the number system. There aren't two proofs, there are two ways of multiplying normal numbers by 10. One is to add a zero at the end of it and shift it up. What is actually happening is that we are shifting the numbers up a column which has the result (in the case of finitely long strings of numbers) of adding a zero at the end. It has been dealt with by others, but I will do it again if you like.x=0.333...
10x= 3.333...10x-x = 9x9x = 3x = 3/9Therefore x =0.333... That doesn't make sense to me at all, the only way to do it would be to flip the equations around. If flipping the equations couldn't prove the converse concept, then there would be a contradiction and the maths would be wrong somewhere.

I'm not sure what you mean..... Infinity is a mathematical concept that has been defined by humans. It certainly does exist as a mathematical concept and is perfectly valid. Infinity (when discussing mathematics) is like an imaginary number.... it's something we have given a definition to because it is a useful concept.There is no question of infinity existing in a mathematical sense.

Mod made an error in his reply mentioning a "zero" there won't be one. There is NO LAST DIGIT. We only write as many as is convenient to show what we mean. (0.9..., 0.99..., 0.999999... or whatever). They are all the same; an endless row of 9's. Trust me, you don't yet.

Some quotes from the link you provided.

quote:

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Other notions associated with infinity are indefinite-
ness and inconceivability.

​

The Greek word for infinity was apeiron, which lit-
erally means unbounded, but can also mean infinite, indefinite, or unde-
fined.

​

There was no place for the apeiron in the universe of Pythagoras and
Plato.

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In order to avoid these actual infinites that seemed to threaten the or-
derliness of his a priori finite world, Aristotle invented the notion of the
potentially infinite as opposed to the actually infinite.

​

This is a doubtful distinction, and I am inclined to agree
with Cantor's opinion that ". . . in truth the potentially infinite has
only a borrowed reality, insofar as a potentially infinite concept always
points towards a logically prior actually infinite concept whose existence
it depends on.

​

2. Consider a very durable ceiling lamp that has an on-off pull string. Say that
the string is to be pulled at noon every day, for the rest of time. If the
lamp starts out off, will it be on or off after an infinite number of days have
passed?

​

2. There are, however, no conclusive proofs that everything is finite; and the
question of whether or not anything infinite exists remains as an open, al-
most empirical problem.

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Infinity is just as subjective as God.Since we really don't understand it, how can we pretend to use it in an equation.Every single equation in this thread the uses some sort of notation for infinity, is using a finite symbol to represent something that is infinite. It's like putting infinity in a box, it can't be done.Does .999.. = 1 ?To me, only if .999... rpresents 3/3, but not by itself does .999... represent 1.The problem is in our number system, it can't handle it. There is no way to express 1/3 of 1 in decimals.

Maybe you don't get what I am saying?I get it, believing .999... = 1 requires a leap of faith.

That is why I mentioned:
Even if we did do it simultaneously,There is no end to the number, so there is no end to the equation.You cannot use the word "all" to describe infinity, What is all + 1 ?

Why not? Because there is no end? Seems like infinity cannot be treated as a number at all. To me adding a zero at the end is just as essential. Ok, I did it wrong. I don't know what happens, but everytime I try to do math on this forum, I screw up. I hate that, I am better than that.Even still, using your answer, 0.333...=0.333... makes more sense. The result seems to be different than 0.999... = 1
Why doesn't 0.333... = 0.4 ?I asked a question earlier, I got answer, but I am not sure I like it, since it came from a calculator. Can you multiply 2 numbers and get .999... ?What is 2 x .999...?

Nope, not this time. This time we are dealing with math and we do prove things.There is no faith. The proof has been shown to you. You do, indeed, not get it. This was answered many posts ago. It is still all.However, here we aren't talking about an infinite quantity (this was pointed out to you before too). We are talking about a representation of a finite quantity that has an infinite number of digits in it.Edited by NosyNed, : fixed spelling

I am not the only to think this.

No, you STILL DON'T understand.Infinity is simply an abstract mathematical concept that WE have defined.There is no leap of faith. You are confusing some generic concept of inifinity with the mathematical definition of infinity..9999............ = 1 is true under the system of mathematics that humans have defined for our use. There is no leap of faith or anythiing. It's like an imaginary number. It exists in our system of mathematics under definitions we have created for it.

Then you missed the point entirely.Numbers do not have ends or beginnings. Those are not properties of numbers. Strings of digits may have ends or beginnings. But the numbers they represent do not.You need to make a distinction between numbers, and strings of digits.The string 0.999... does represent a number. And the reason it respresents a number, is that we have well established conventions that specify how strings of digits can represent numbers. These conventions extend to infinite decimal representations.

10/3 can be represented by decimals. 10/3 is just more conrete..99999999999999999999 does equal 3/3..33333333333333333333 = 1/3..33333333333333333333 * 3 = .999999999999999999999
.33333333333333333333 * 3 = 3/3 = 1.
assume all the long decimals strecth for infinity.this means that 3/3 = .999999999999999999999999, which means that .99999999999999999999 = 1.if A = B, and B = C, then A = c.
if (A).99999999999999999999999999 = (B)3/3, and (B)3/3 = (C)1, then (A).999999999999999999999 = (C)1.Edited by kuresu, : fixed logic proof, so that A = C, instead of A =B at the end.

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All a man's knowledge comes from his experiences

Have you ever taken Calculus or studied infinite series? If not, I can totally understand how some of this wouldn't make sense.The proof of .9999.............. = 1 using the limit of a converging series is rock solid. Once you can understand that proof everything will make sense to you.Maybe this will help:http://www.math.utah.edu/...on/teaching/calculus/series.htmlThe key to all this is that .9999...... is a CONVERGENT series.http://www.maths.abdn.ac.uk/.../tch/ma2001/notes/node49.htmlHere's one more page on it...Series - Wikipedia(mathematics)

I'll amswer both questions.what times 2 = .99999999999999999999999999?
.5 * 2 = .999999999999999999999999999,
because .999999999999999999999 = 1.99999999999999999999999 * 2 = ?
.99999999999999999999= 2,
because .9999999999999999999 = 1.Anywho, these calculators have been programmed by mathemiticians and are notorious for getting the right answer.So I'll trust them to get the answer to whatever I put in them. I just have to put in the right data.

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All a man's knowledge comes from his experiences

Your right, partially. I do get the proof. I am questioning it.I have always thought that if .333... can = 1/3, then .999... can equal 1. It makes perfect sense. But not from the equation that mod provided. Not yet anyway.I will ask you also, what is 2*.999... ? Ok, I stand corrected. The definition of all is not limited to a finite number. Yes, I realize the difference. There has been some confusion between the two in this thread. However, I do not understand you describing it as a finite quantity, if we actually cannot know what that quantity is, only that it goes on forever. It is infinitly increasing in resolution.