.9999.... Repeating Does Equal 1

[Fonceai]

@gr8fuldaniel

1/3 ≠ 0.3r : true
1/3 = 0.3r : false
1/3 ≈ 0.3r : true
1/3 = ~0.3r : true

But you basically have it right with your other example.

1 - 0.9 = 0.1
1 - 0.99 = 0.01
...and so on.

The trailing 1 you are referring to is expressed with 1 / ∞

[gr8fuldaniel]

@gr8fuldaniel

1/3 ≠ 0.3r : true
1/3 = 0.3r : false
1/3 ≈ 0.3r : true
1/3 = ~0.3r : true

I never said anything different from that.
Except, I am not sure about how the last one is true "1/3 = ~0.3r : true"

How could a string of ininite whole zeros (on the positive side) change the equation from ≠ (to =) in the 1st example?

[Fonceai]

Except, I am not sure about how the last one is true

I'll write out each of the four in prose:

One-third does not equal point three repeating: that is true.

One-third equals point three repeating: that is false.

One-third is approximately equal to point three repeating: that is true.

One-third equals approximately point three repeating: that is true.

[gr8fuldaniel]

One-third equals approximately point three repeating: that is true.

Thats the problem.

I understand ≈ means "equals approximately" see my quote above"

wiki

A symbol used to denote items that are approximately equal is ≈,

I thought I saw ~ used as a symbol for infinity somewhere.
My character code chart doesnt have a symbol for the sideways 8. MY MISTAKE, I should have just used "r...".

tilde
Mathematics
In mathematics, the tilde, often pronounced "twiddle," is often used to denote an equivalence relation between two objects. Thus x ~ y means x "is equivalent to" y (Note that this is quite different from stating that x equals y.)

This page says ~ means "Similar to", and
≈ Means "Approximately" (the HTML is alt 247)

I will have to look for the code for "sideways eight" later.

[Fonceai]

says ~ means "Similar to", and
≈ Means "Approximately

I agree with that.

Remember that ≈ is used in place of the equal sign.

~ is used in front of a value.

Your quote is correct in stating the difference between equivalence and equality.

The language of math is very specific and unforgiving.

[Compugasm]

.9r doesn't seem to equal 1, until you try to do maths on it.

[gr8fuldaniel]

equal means identical. They dont even look alike. .9r = .9r and 1=1

Look at the "maths" again. It dont add up.
If he uses rounding off in his equation it invalidates the whole damn formula.

[gr8fuldaniel]

The language of math is very specific and unforgiving.

I wonder why we cant have access to all the characters on our keyboards?
Maybe Scribbler or Compugasm can work on that....
A maybe a little accessory keypad with USB that you can plug into the back of your keyboard (if microsoft cant make it happen, somebody should.) You could have different software for smilies and stuff too. People would buy it.

[Fonceai]

Because not all characters have an ASCII code, and I forget how to enter text unicode. Just have to use the "charmap" and Select - Copy for now.

[Kamehameha34]

I just think of this as proof that infinity can't exist, only be approached.

[Fonceai]

Some would argue that you can never approach infinity, since it never ends.

No matter how far you go, infinity is always an infinite distance ahead of you.

That's why I don't like Cantor sets... he assigns quantity to the unquantifiable.

[Castle]

anybody else see any contradictions?

Either make your case or don't, but don't make vague statements accusing me of contradiction. This is mathematics. I have provided a proof. You have not addressed it. Until addressed, the proof stands It's really that simple.

It would be safe to reason there would be a 1 at the end of an infinite string.

Repeat after me: An infinite string has no end. Hence the "infinite".

You try to prove otherwise with complicated formulas that contain blatant flaws that require even more rounding off.

To date, you have posted 28 times in this thread. You have yet to identify a single "blatant flaw" in any of the "complicated formulas". Come on; you made a claim. Prove it.

As long as you maintain order of operations, you should get the same answers every time. I showed that you don't.

Circular reasoning. If .9r (and x) do equal 1, then 9x=9 is identical to 9=9. You're assuming what you want to prove in attempting to prove it.

Even if we were to accept your reasoning, what you've shown would be a contradiction in mathematics, not the proof. You need to address the proof on its own terms and show how it is mathematically invalid. Merely saying "It must be because of this" doesn't cut it.

You have still failed to show a flaw in the proof, despite all this talk of approximations. You don't need to reply in a long post about approximations, equality, how math is a language, or how formulas are "fudging". You need to quote one of the steps in the proof and show how it is mathematically invalid. Nothing more, and nothing less.