Does 0.9999 repeating 9 equal 1?

[PeterMP]

Okay. I guess I'm confusing "set" for "value."

You're right.

If you have that, try this. Pick two points in space (literally stick two different fingers in the air). We could measure the distance between them, and it must be finite (unless you have an infinitely long arm or the combination of your arms are infinitely long). BUT those two points are separated by an infinite number of points.

[PokerPacker]

Okay. Find a fault with this:

the fault with that is that its not real math. you can't just put a "..." in the middle of a solid number and manipulate it. the point of the Riemann Sums I've been using is to create an infinite recursion to express it. The degree of infinity (yes that is a real thing) IS important and people keep not factoring it in. 9.99 is the third degree to infinity of 10x. .999 is the third degree to infinity of x. subtract those and you will get 8.991. the next if you include the next degree of infinity of both, because you have to keep to the same degree of infinity, then the next solution will be 8.9991. You will be left with this will leave you with a series that the limit as n, being the degree to infinity, approaches infinity, is 9. which, as I've stated multiple times, brings us right back to where we started.

[Larry]

.3 repeating is not exactly one third. It's just the closest number to 1/3 that we use for simplicity.

.3 repeating is exactly 1/3.

As will be obvious if you attempt to use long division on it.

[Mark The Homer]

PP - What is wrong with this:

If .333 (repeating) is exactly one-third.

Then .999 (repeating) has to be exactly three-thirds.

And three-thirds = one.

credit: Thinking Skins

Is this also not real math?

[PokerPacker]

PP - What is wrong with this:

If .333 (repeating) is exactly one-third.

Then .999 (repeating) has to be exactly three-thirds.

And three-thirds = one.

credit: Thinking Skins

Is this also not real math?

the limit as the number of integers of .333 approaches infinity is 1/3

the limit as the number of integers of .999 approaches infinity is 1

[Mark The Homer]

If you have that, try this. Pick two points in space (literally stick two different fingers in the air). We could measure the distance between them, and it must be finite (unless you have an infinitely long arm or the combination of your arms are infinitely long). BUT those two points are separated by an infinite number of points.

I'm fine with that. And I can see where you're going. Point taken. Thank-you :thumbsup:

[Mark The Homer]

PP - What is wrong with this:

If .333 (repeating) is exactly one-third.

Then .999 (repeating) has to be exactly three-thirds.

And three-thirds = one.

credit: Thinking Skins

Is this also not real math?

the limit as the number of integers of .333 approaches infinity is 1/3

the limit as the number of integers of .999 approaches infinity is 1

I'm not talking about limits. I'm talking about finite numbers.

Look at it again.

[PeterMP]

the limit as the number of integers of .333 approaches infinity is 1/3

the limit as the number of integers of .999 approaches infinity is 1

Right, but what if you are at infinity. You've quit approaching it and have reached it.

[PokerPacker]

I'm not talking about limits. I'm talking about finite numbers.

Look at it again.

you are obviously not talking about finite numbers when you specify they continue on to infinity.

[Mark The Homer]

you are obviously not talking about finite numbers when you specify they continue on to infinity.

Are you serious.

I thought we already established that .3333 repeating was one-third, which is a finite value.

Yes or no?

Did I confuse you by using "numbers" instead of "values"? If so, sorry, I'm not a mathematician. I'm probably confusing the terms, but I think you understand where I'm going.

Edit: Reading my post, I didn't use the term "numbers." You did. It almost sounds like you're purposely refusing to accept the truth when it's staring you in the face.

[Elessar78]

I think this thread is approaching ITS limit!

19 pages! C'mon people.

[Mark The Homer]

PP - Let's stop using the word numbers and start using the word values.

Is .333 repeating not a finite value?

[PokerPacker]

Are you serious.

I thought we already established that .3333 repeating was one-third, which is a finite value.

Yes or no?

.3333 repeating is not a finite value. by definition it is an infinite value. the limit as the number of digits reaches infinity would be 1/3, but that is exactly the same problem as the initial question which means we've gotten nowhere.

[PokerPacker]

PP - Let's stop using the word numbers and start using the word values.

Is .333 repeating not a finite value?

no, .333 repeating is not a finite value. by definition, if it takes infinity to get its true value, it cannot be finite.

[Mark The Homer]

.3333 repeating is not a finite value. by definition it is an infinite value. the limit as the number of digits reaches infinity would be 1/3, but that is exactly the same problem as the initial question which means we've gotten nowhere.

I'll accept that. We've gotten nowhere. lol

You keep talking about the limit. I strongly believe you are using the word "limit" incorrectly.

.333 repeating is a finite value. It's one-third. There is nothing infinite about one-third.

Just because we happen to have a base ten number system which requires us to use infinite trailing 3's to express one-third in decimal form does not disqualify it from having a finite value of one-third.

You are confusing

"infinite" as it is used to express a decimal number with trailing digits

with

"infinite" as a value.

It's two different things.

[Larry]

See how annoying that is? Where does .3 repeating end if it's finite?

I suggest you examine what it is that makes a number finite.

It isn't how much paper it takes to write it down.

[PokerPacker]

I'm gonna be honest, I've been exhausted of this subject. We (not you and I, but side A and side keep arguing the same points with different values and aren't getting anywhere. I figure I'll limit myself, as this thread approaches infinity, to only 20 pages .

[Larry]

Edit: See, now you got me writing like Larry

I don't think I've ever used that goofy smiley.

[Larry]

I think this is a situation I can choose to be ignorant of, and not experience any repercussions. This debate is without bounds.

BTW, if I wanted to say that a value approaches one but never actually reaches it (as in a function), what number would I use?

You cannot use a number, you have to use an experssion.

Numbers don't approach anything. Numbers are.

[Mark The Homer]

I'm gonna be honest, I've been exhausted of this subject. We (not you and I, but side A and side keep arguing the same points with different values and aren't getting anywhere. I figure I'll limit myself, as this thread approaches infinity, to only 20 pages .

Fine - but you have to admit - the odds of you being correct are not good - considering virtually everybody in this thread has seen the light except you.

Take care.

[Thinking Skins]

the limit as the number of integers of .333 approaches infinity is 1/3

the limit as the number of integers of .999 approaches infinity is 1

what you said makes no sense -

"as the number of integers of"

every decimal number has an infinite number of digits. It just so happens that a lot of the numbers are 0.

The sum of .3 + .03 + .003 + ... + 3*10^-k as k approaches infinity is 1/3.

Thats the same as saying that .33333 (repeating) is 1/3.

Its the definition of a sum converging to a number. It means that we can write the sum on the left hand side, and then an equal sign, and then what it converges to on the right hand side.

ala, because (as you agree) the limit of the .333 as the number of digits approaches infinity is 1/3, we can say that

\sum_{k = 1 to \inf} (3*10^-k) converges to 1/3,

which by definition of convergence we can write

\sum_{k = 1 to \inf} (3*10^-k) = 1/3,

which because we write .333333... as the shorthand (decimal) way of writingthe summation on the left hand side, so we can replace it with

.3333.... = 1/3.

Then we can multiply both sides by 3 to get

.9999.... = 1

[Mark The Homer]

I don't think I've ever used that goofy smiley.

So - that would be an infinitely small number of times?

[Hubbs]

This thread:

[PokerPacker]

Fine - but you have to admit - the odds of you being correct are not good - considering virtually everybody in this thread has seen the light except you.

Take care.

Well the majority of the world believes in a deity of some sort and the majority of the country votes for a Democrat or Republican, that doesn't stop me from going my own way.

[Mark The Homer]

Well the majority of the world believes in a deity of some sort and the majority of the country votes for a Democrat or Republican, that doesn't stop me from going my own way.

But you're never going to vote for a president who wins.