5 ms·

Yes, '0.999...' formally stands for the sum from n = 1 to infinity of 9 / 10^n.

by cgmg 9y ago

KGIII 9y ago
Heh... You kinda prove my point for me. If you could step up to the board and actually expand the ... for us, we'd be much obliged. You can keep writing 9 forever and you will never reach a whole number. But, it does reach a whole number and there is proof! So, they made a rule. The rule is, of course, silly. Infinity itself is silly. Not even atoms are infinite. Not even atoms can be infinity divisible. It's a horrible idea, really. (I have karma to burn.) By the way, it's a damned good thing infinity doesnt exist. If you had a tape measure that was infinitely long and folded it in half, we aren't really sure what would happen. Hell, I wasn't using that karma for anything better. While I'm here... When you're done finding an infinite tape measure, I'd like it if you could bring me -1 apple. No, not a slip of paper representing an owed apple, but -1 apple. Math and reality are only loosely coupled. Mathematics is a language. It can tell lies. 1 + 1 = 74 See? That's pretty obviously a lie. It can tell stories, physicists are pretty fond of using it for that. It can be so very descriptive and elegant. It can be so deceptive, as we see with the 'well, let's just let that be represented by 9/10' silliness. It's pretty horrible, really. Like I said, it's best not to think about it too much. It's kind of contrived in a few areas.
- cgmg 9y ago
  > If you could step up to the board and actually expand the ... for us, we'd be much obliged. It seems you don't know what a sequence is. A sequence is just a function whose codomain is the natural numbers, i.e. you give any natural number you choose, and I give you the corresponding digit. I don't need to 'expand' the ellipses to define that function, any more than I have to write down all perfect squares in order to define what a perfect square is. Seriously, this is basic mathematics. You should study it before publicly embarrassing yourself by calling mathematicians 'liars'.
  - KGIII 9y ago
    I do understand it. In fact, I understand it quite well. I can give you the textbook definitions. I've studied them completely. I hold a Ph.D., you know. You are accepting rote still, as opposed to concerning yourself with the Philosophy of Mathematics. The ... represents an infinitely repeating numeral, does it not? It is a shorter way of writing 0.999999999999 (into infinity). Now, you can do that forever and you will never reach a whole number. Ever... Go ahead, try it. I'll wait. So, we've all happily agreed on some very contrived rules that you'll quote verbatim and gleefully declare to be basic mathematics and I the embarrassment. You'll commit no more thought to the process and, as I've already stated, that's a very good choice. (Karma for days...)
    - cgmg 9y ago
      > Now, you can do that forever and you will never reach a whole number. Ever... Go ahead, try it. I'll wait. What in the world are you rambling about? Do you know what a limit is? > I hold a Ph.D., you know. Yeah, and I'm the king of France. If you really have a Ph.D., I'd wager it's not in mathematics, given the content of your posts.
      - Simon_says 9y ago
        I, on the other hand, would bet KGIII's Ph.D. is in math. I have a Ph.D. in math, too, and I've met, shall we say, a wide variety of fellow Ph.D. holders.
      - KGIII 9y ago
        You have given me one of the best chuckles I've had in weeks. Thanks! Err... If you really wanted, you could probably use a search engine and figure out who I am. I actually am a mathematician. But, you can keep your wager.
        cgmg 9y ago
        > I actually am a mathematician. But you don't know what a limit is?
- perl4ever 9y ago
  Regarding -1 apple, you can argue in the same way that any concept "doesn't exist" if you refuse to recognize a correspondence between it and its referent. What makes "-1 apple" less real than "1 apple"? I could argue, for example, that the conceptual boundary between an apple and the tree it came from cannot be guaranteed to be the same as its actual physical point of separation, and thus any real apple is more like 1.000001 or 0.99999 apples, so there is no such thing as "1 apple" in reality.
  - KGIII 9y ago
    Oh! I like that. I will counter that I can hold what I believe to be an apple, or close enough to being a single apple. I can not do so with a -1 apple. Horrible, really. ;-)
enord 9y ago
Oh, well then could you point me to a formal definition of the syntax and semantics for the unary "..." operator then? What is then domain and codomain, for example? Much obliged.
- cgmg 9y ago
  ... is not an operator.

Yes, '0.999...' formally stands for the sum from n = 1 to infinity of 9 / 10^n.

by cgmg 9y ago

Yes, '0.999...' formally stands for the sum from n = 1 to infinity of 9 / 10^n.

Heh... You kinda prove my point for me. If you could step up to the board and actually expand the ... for us, we'd be much obliged. You can keep writing 9 forever and you will never reach a whole number. But, it does reach a whole number and there is proof! So, they made a rule. The rule is, of course, silly. Infinity itself is silly. Not even atoms are infinite. Not even atoms can be infinity divisible. It's a horrible idea, really. (I have karma to burn.) By the way, it's a damned good thing infinity doesnt exist. If you had a tape measure that was infinitely long and folded it in half, we aren't really sure what would happen. Hell, I wasn't using that karma for anything better. While I'm here... When you're done finding an infinite tape measure, I'd like it if you could bring me -1 apple. No, not a slip of paper representing an owed apple, but -1 apple. Math and reality are only loosely coupled. Mathematics is a language. It can tell lies. 1 + 1 = 74 See? That's pretty obviously a lie. It can tell stories, physicists are pretty fond of using it for that. It can be so very descriptive and elegant. It can be so deceptive, as we see with the 'well, let's just let that be represented by 9/10' silliness. It's pretty horrible, really. Like I said, it's best not to think about it too much. It's kind of contrived in a few areas.

cgmg 9y ago
> If you could step up to the board and actually expand the ... for us, we'd be much obliged. It seems you don't know what a sequence is. A sequence is just a function whose codomain is the natural numbers, i.e. you give any natural number you choose, and I give you the corresponding digit. I don't need to 'expand' the ellipses to define that function, any more than I have to write down all perfect squares in order to define what a perfect square is. Seriously, this is basic mathematics. You should study it before publicly embarrassing yourself by calling mathematicians 'liars'.
- KGIII 9y ago
  I do understand it. In fact, I understand it quite well. I can give you the textbook definitions. I've studied them completely. I hold a Ph.D., you know. You are accepting rote still, as opposed to concerning yourself with the Philosophy of Mathematics. The ... represents an infinitely repeating numeral, does it not? It is a shorter way of writing 0.999999999999 (into infinity). Now, you can do that forever and you will never reach a whole number. Ever... Go ahead, try it. I'll wait. So, we've all happily agreed on some very contrived rules that you'll quote verbatim and gleefully declare to be basic mathematics and I the embarrassment. You'll commit no more thought to the process and, as I've already stated, that's a very good choice. (Karma for days...)
  - cgmg 9y ago
    > Now, you can do that forever and you will never reach a whole number. Ever... Go ahead, try it. I'll wait. What in the world are you rambling about? Do you know what a limit is? > I hold a Ph.D., you know. Yeah, and I'm the king of France. If you really have a Ph.D., I'd wager it's not in mathematics, given the content of your posts.
    - Simon_says 9y ago
      I, on the other hand, would bet KGIII's Ph.D. is in math. I have a Ph.D. in math, too, and I've met, shall we say, a wide variety of fellow Ph.D. holders.
    - KGIII 9y ago
      You have given me one of the best chuckles I've had in weeks. Thanks! Err... If you really wanted, you could probably use a search engine and figure out who I am. I actually am a mathematician. But, you can keep your wager.
      - cgmg 9y ago
        > I actually am a mathematician. But you don't know what a limit is?
perl4ever 9y ago
Regarding -1 apple, you can argue in the same way that any concept "doesn't exist" if you refuse to recognize a correspondence between it and its referent. What makes "-1 apple" less real than "1 apple"? I could argue, for example, that the conceptual boundary between an apple and the tree it came from cannot be guaranteed to be the same as its actual physical point of separation, and thus any real apple is more like 1.000001 or 0.99999 apples, so there is no such thing as "1 apple" in reality.
- KGIII 9y ago
  Oh! I like that. I will counter that I can hold what I believe to be an apple, or close enough to being a single apple. I can not do so with a -1 apple. Horrible, really. ;-)

enord 9y ago

Oh, well then could you point me to a formal definition of the syntax and semantics for the unary "..." operator then? What is then domain and codomain, for example? Much obliged.

cgmg 9y ago
... is not an operator.