June 2, 2011 at 9:38 am
So, I put this up on a white board which has started some pretty intense conversations.
.999... = 1
I'd like to see how other DBAs view this equation whether you think it's true or not and why.
I know there's some mathematicians here too, will be interesting to hear your take on the equation.
go!
June 2, 2011 at 10:23 am
That brings up memories. 🙂 We had the same whiteboard discussion about 3 years ago at my old workplace. At that time, I was (ignorantly) on the against side. I think the human mind just doesn't want to make sense of non-terminating decimals, so we naturally don't want to accept that equality. Although, no one argues that 1/9 = 0.111... isn't true...which is equivalent to 0.999... = 1. 😉
______________________________________________________________________________
How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics.
June 2, 2011 at 10:37 am
Of course it's true, so long as the ellipse there really means "repeating more nines infinitely".
1/3*3=1
Anyone care to argue with that?
A=B
B=C
hence A=C
Anyone care to argue with that?
If those are true, then syllogistically, .9... = 1.
The thing to keep in mind is that numbers are an abstract symbol for something that doesn't really exist. There is no "1" in the physical universe, and there definitely is no situation where 1 of something = 1 of anything. Even a thing is only actually equal to itself at a specific instant in time. "One" of any time unit earlier or later, it's not actually fully equal.
Math is a language. It makes the pretense, in non-professional circles, of being "exact", when truly it is merely "precise". 1 = 1 if and only if we're not talking about actual values. 0 does, however, actually equal 0, but only when applied to statements of complete lack of existence.
It gets more fun from there. 🙂
- Gus "GSquared", RSVP, OODA, MAP, NMVP, FAQ, SAT, SQL, DNA, RNA, UOI, IOU, AM, PM, AD, BC, BCE, USA, UN, CF, ROFL, LOL, ETC
Property of The Thread
"Nobody knows the age of the human race, but everyone agrees it's old enough to know better." - Anon
June 2, 2011 at 10:55 am
GSquared (6/2/2011)
Of course it's true, so long as the ellipse there really means "repeating more nines infinitely". ...
yes the elipses is meant as infinite.
GSquared (6/2/2011)
... 0 does, however, actually equal 0, but only when applied to statements of complete lack of existence.
null?
1-1=null?
June 2, 2011 at 11:14 am
Per http://www.thefreedictionary.com/null, yes, since null is a synonym for zero.
However, most DBAs would assume that null = no assigned value, not null = 0 (linguistic equality as well as mathematic, in this case). Zero has an assigned value, Null may not, depending on which definition of "null" you are using. Since that enters an ambiguity into the language, and mathematics is a language designed to minimize ambiguity, I would say don't use "1-1=null", not because it's wrong, but because it's ambiguous in meaning.
To clarify absolute lack of existence as expressed by "zero": Think of the English-language statement "I have no apples". That means you don't have any apples. But is it truly zero? If, for example, you have eaten an apple, or anything that has ever been in proximity to an apple, your body probably has molecules in it that were, at one point in time or another, part of an apple. Does that mean that, rather than absolute-zero, you actually have some infinitely small fraction of one or more apples?
If the local grocery store has apples, and you have money, then you have "potential apples". How does zero relate to that?
If, on the other hand, you can make the statement, "at this time, I not have within the reach of my hands, any whole apples", this is a statement of absolute non-existence, and thus absolute-zero applies to it.
Conversely, if you are holding an apple in your hand, and you state, "at this time, I have in my hand, exactly one apple", it's still not absolute-one (comparable to absolute-zero). This is simple due to the fact that "apple" is, in essence, an ambiguity that encompasses a wide variety of human experiences that are composited into the force-language-abstract, in English, of "apple".
This is due to the basic nature of language, for one thing. (All words are simply agreements that certain perceptions of force have congruence/coincidence/causation.) It's also due to the fact that the apple itself changes from moment to moment, and is also only comparable to other apples using vague margins of error.
There, you ask for DBAs and mathematicians, and you get linguistics and philosophy as well. 🙂
- Gus "GSquared", RSVP, OODA, MAP, NMVP, FAQ, SAT, SQL, DNA, RNA, UOI, IOU, AM, PM, AD, BC, BCE, USA, UN, CF, ROFL, LOL, ETC
Property of The Thread
"Nobody knows the age of the human race, but everyone agrees it's old enough to know better." - Anon
June 2, 2011 at 12:02 pm
I agree with GSquared on this. It is a difference that makes no practicle difference, at least at this point in time. Quantum physics, for example uses teeny-tiny numbers, but not zeros to infinity then a 1 at the end (but wait, there is no end).
The principle here is the same as in Zeno's paradoxes too.
The greatest enemy of knowledge is not ignorance, it is the illusion of knowledge. - Stephen Hawking
June 2, 2011 at 12:22 pm
GSquared, I think it would be a wonderful thing to sit at a bar and have some beers with you. We would probably spend the whole night debating when a "beer" ceases to be a "beer". 😉 That's the problem I have when anything is broken down philosophically, everything becomes nothing because all the meaning is sucked out. For example, when you say
To clarify absolute lack of existence as expressed by "zero": Think of the English-language statement "I have no apples". That means you don't have any apples. But is it truly zero? If, for example, you have eaten an apple, or anything that has ever been in proximity to an apple, your body probably has molecules in it that were, at one point in time or another, part of an apple. Does that mean that, rather than absolute-zero, you actually have some infinitely small fraction of one or more apples?
So when does an apple stop being an apple? When a bite is taken? When only the core is left? Or when there are only the molecules left that used to composed the apple? See! Something has become nothing and then everything in one swoop! Molecules that were an apple are now muscle tissues in an animal; now they are dirt; now a tree; etc., ad nauseum. Everything that used to be is now everything that is which will be part of everything that will be. This is why these conversations exhaust me. 😛
Reminds me of Richard Feynman's story of the philosophy class asking him about the properties of an atom, whether it was a real thing or abstract. He wanted to simplify the question, so he asked them about the properties of a brick. They spent the rest of the evening arguing among themselves about what constitutes brickness. (Ah, I got some of that wrong, but my meaning is there. Check out the pages here: http://books.google.com/books?id=7papZR4oVssC&pg=PA70&lpg=PA70&dq=feynman+brick&source=bl&ots=esN07crN1-&sig=nVoZ_O3yrxToJxuwV5H8--FD6yM&hl=en&ei=ntLnTbztL4nAtgfoktDnCg&sa=X&oi=book_result&ct=result&resnum=1&sqi=2&ved=0CBoQ6AEwAA#v=onepage&q=feynman%20brick&f=false )
______________________________________________________________________________
How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics.
June 2, 2011 at 12:34 pm
toddasd (6/2/2011)
GSquared, I think it would be a wonderful thing to sit at a bar and have some beers with you. We would probably spend the whole night debating when a "beer" ceases to be a "beer". 😉 That's the problem I have when anything is broken down philosophically, everything becomes nothing because all the meaning is sucked out. For example, when you sayTo clarify absolute lack of existence as expressed by "zero": Think of the English-language statement "I have no apples". That means you don't have any apples. But is it truly zero? If, for example, you have eaten an apple, or anything that has ever been in proximity to an apple, your body probably has molecules in it that were, at one point in time or another, part of an apple. Does that mean that, rather than absolute-zero, you actually have some infinitely small fraction of one or more apples?
So when does an apple stop being an apple? When a bite is taken? When only the core is left? Or when there are only the molecules left that used to composed the apple? See! Something has become nothing and then everything in one swoop! Molecules that were an apple are now muscle tissues in an animal; now they are dirt; now a tree; etc., ad nauseum. Everything that used to be is now everything that is which will be part of everything that will be. This is why these conversations exhaust me. 😛
Reminds me of Richard Feynman's story of the philosophy class asking him about the properties of an atom, whether it was a real thing or abstract. He wanted to simplify the question, so he asked them about the properties of a brick. They spent the rest of the evening arguing among themselves about what constitutes brickness. (Ah, I got some of that wrong, but my meaning is there. Check out the pages here: http://books.google.com/books?id=7papZR4oVssC&pg=PA70&lpg=PA70&dq=feynman+brick&source=bl&ots=esN07crN1-&sig=nVoZ_O3yrxToJxuwV5H8--FD6yM&hl=en&ei=ntLnTbztL4nAtgfoktDnCg&sa=X&oi=book_result&ct=result&resnum=1&sqi=2&ved=0CBoQ6AEwAA#v=onepage&q=feynman%20brick&f=false )
Yes, analytic philosophy can really stink, to put it bluntly. But at the same time, philosophy is one of the few disciplines that allow us to ask all the BIG questions, like "What is truth?", "Why are we here?" and "How much wood would a woodchuck chuck if a woodchuck could chuck wood?"
The greatest enemy of knowledge is not ignorance, it is the illusion of knowledge. - Stephen Hawking
June 2, 2011 at 1:30 pm
mtillman-921105 (6/2/2011)
toddasd (6/2/2011)
GSquared, I think it would be a wonderful thing to sit at a bar and have some beers with you. We would probably spend the whole night debating when a "beer" ceases to be a "beer". 😉 That's the problem I have when anything is broken down philosophically, everything becomes nothing because all the meaning is sucked out. For example, when you sayTo clarify absolute lack of existence as expressed by "zero": Think of the English-language statement "I have no apples". That means you don't have any apples. But is it truly zero? If, for example, you have eaten an apple, or anything that has ever been in proximity to an apple, your body probably has molecules in it that were, at one point in time or another, part of an apple. Does that mean that, rather than absolute-zero, you actually have some infinitely small fraction of one or more apples?
So when does an apple stop being an apple? When a bite is taken? When only the core is left? Or when there are only the molecules left that used to composed the apple? See! Something has become nothing and then everything in one swoop! Molecules that were an apple are now muscle tissues in an animal; now they are dirt; now a tree; etc., ad nauseum. Everything that used to be is now everything that is which will be part of everything that will be. This is why these conversations exhaust me. 😛
Reminds me of Richard Feynman's story of the philosophy class asking him about the properties of an atom, whether it was a real thing or abstract. He wanted to simplify the question, so he asked them about the properties of a brick. They spent the rest of the evening arguing among themselves about what constitutes brickness. (Ah, I got some of that wrong, but my meaning is there. Check out the pages here: http://books.google.com/books?id=7papZR4oVssC&pg=PA70&lpg=PA70&dq=feynman+brick&source=bl&ots=esN07crN1-&sig=nVoZ_O3yrxToJxuwV5H8--FD6yM&hl=en&ei=ntLnTbztL4nAtgfoktDnCg&sa=X&oi=book_result&ct=result&resnum=1&sqi=2&ved=0CBoQ6AEwAA#v=onepage&q=feynman%20brick&f=false )
Yes, analytic philosophy can really stink, to put it bluntly. But at the same time, philosophy is one of the few disciplines that allow us to ask all the BIG questions, like "What is truth?", "Why are we here?" and "How much wood would a woodchuck chuck if a woodchuck could chuck wood?"
1) It's what we agree it is
2) Because it's more fun than not being here
3) A woodchuck would chuck all the wood he could chuck if a woodchuck could chuck wood
- Gus "GSquared", RSVP, OODA, MAP, NMVP, FAQ, SAT, SQL, DNA, RNA, UOI, IOU, AM, PM, AD, BC, BCE, USA, UN, CF, ROFL, LOL, ETC
Property of The Thread
"Nobody knows the age of the human race, but everyone agrees it's old enough to know better." - Anon
June 2, 2011 at 1:36 pm
toddasd (6/2/2011)
GSquared, I think it would be a wonderful thing to sit at a bar and have some beers with you. We would probably spend the whole night debating when a "beer" ceases to be a "beer". 😉 That's the problem I have when anything is broken down philosophically, everything becomes nothing because all the meaning is sucked out. For example, when you sayTo clarify absolute lack of existence as expressed by "zero": Think of the English-language statement "I have no apples". That means you don't have any apples. But is it truly zero? If, for example, you have eaten an apple, or anything that has ever been in proximity to an apple, your body probably has molecules in it that were, at one point in time or another, part of an apple. Does that mean that, rather than absolute-zero, you actually have some infinitely small fraction of one or more apples?
So when does an apple stop being an apple? When a bite is taken? When only the core is left? Or when there are only the molecules left that used to composed the apple? See! Something has become nothing and then everything in one swoop! Molecules that were an apple are now muscle tissues in an animal; now they are dirt; now a tree; etc., ad nauseum. Everything that used to be is now everything that is which will be part of everything that will be. This is why these conversations exhaust me. 😛
Reminds me of Richard Feynman's story of the philosophy class asking him about the properties of an atom, whether it was a real thing or abstract. He wanted to simplify the question, so he asked them about the properties of a brick. They spent the rest of the evening arguing among themselves about what constitutes brickness. (Ah, I got some of that wrong, but my meaning is there. Check out the pages here: http://books.google.com/books?id=7papZR4oVssC&pg=PA70&lpg=PA70&dq=feynman+brick&source=bl&ots=esN07crN1-&sig=nVoZ_O3yrxToJxuwV5H8--FD6yM&hl=en&ei=ntLnTbztL4nAtgfoktDnCg&sa=X&oi=book_result&ct=result&resnum=1&sqi=2&ved=0CBoQ6AEwAA#v=onepage&q=feynman%20brick&f=false )
It really becomes simplified if you understand that philosophy is recursive. Want to confuse amateurs in that field, just as "What is philosophy?" Watch them fumble around for a while until they realize they're in Plato's Cave, just like everyone else.
- Gus "GSquared", RSVP, OODA, MAP, NMVP, FAQ, SAT, SQL, DNA, RNA, UOI, IOU, AM, PM, AD, BC, BCE, USA, UN, CF, ROFL, LOL, ETC
Property of The Thread
"Nobody knows the age of the human race, but everyone agrees it's old enough to know better." - Anon
June 2, 2011 at 1:39 pm
1/9 = .111...
9*(1/9) = .999...
9*(1/9) = 1, therefore 1 = .999...
Other proofs here:
http://en.wikipedia.org/wiki/0.999...
I'm waiting for Jeff Moden to supply a proof using a tally table. 😎
June 2, 2011 at 1:45 pm
toddasd (6/2/2011)
GSquared, I think it would be a wonderful thing to sit at a bar and have some beers with you. We would probably spend the whole night debating when a "beer" ceases to be a "beer". 😉
Oh, and on the beer thing, my only philosophy on beer is that the human kidney is the world's most efficient machine for turning European beer into American beer.
Honestly though, I'm going to take that whole bit as a compliment. Thank you.
And, yes, I love discussing things like this.
- Gus "GSquared", RSVP, OODA, MAP, NMVP, FAQ, SAT, SQL, DNA, RNA, UOI, IOU, AM, PM, AD, BC, BCE, USA, UN, CF, ROFL, LOL, ETC
Property of The Thread
"Nobody knows the age of the human race, but everyone agrees it's old enough to know better." - Anon
June 2, 2011 at 1:58 pm
GSquared (6/2/2011)
mtillman-921105 (6/2/2011)
toddasd (6/2/2011)
GSquared, I think it would be a wonderful thing to sit at a bar and have some beers with you. We would probably spend the whole night debating when a "beer" ceases to be a "beer". 😉 That's the problem I have when anything is broken down philosophically, everything becomes nothing because all the meaning is sucked out. For example, when you sayTo clarify absolute lack of existence as expressed by "zero": Think of the English-language statement "I have no apples". That means you don't have any apples. But is it truly zero? If, for example, you have eaten an apple, or anything that has ever been in proximity to an apple, your body probably has molecules in it that were, at one point in time or another, part of an apple. Does that mean that, rather than absolute-zero, you actually have some infinitely small fraction of one or more apples?
So when does an apple stop being an apple? When a bite is taken? When only the core is left? Or when there are only the molecules left that used to composed the apple? See! Something has become nothing and then everything in one swoop! Molecules that were an apple are now muscle tissues in an animal; now they are dirt; now a tree; etc., ad nauseum. Everything that used to be is now everything that is which will be part of everything that will be. This is why these conversations exhaust me. 😛
Reminds me of Richard Feynman's story of the philosophy class asking him about the properties of an atom, whether it was a real thing or abstract. He wanted to simplify the question, so he asked them about the properties of a brick. They spent the rest of the evening arguing among themselves about what constitutes brickness. (Ah, I got some of that wrong, but my meaning is there. Check out the pages here: http://books.google.com/books?id=7papZR4oVssC&pg=PA70&lpg=PA70&dq=feynman+brick&source=bl&ots=esN07crN1-&sig=nVoZ_O3yrxToJxuwV5H8--FD6yM&hl=en&ei=ntLnTbztL4nAtgfoktDnCg&sa=X&oi=book_result&ct=result&resnum=1&sqi=2&ved=0CBoQ6AEwAA#v=onepage&q=feynman%20brick&f=false )
Yes, analytic philosophy can really stink, to put it bluntly. But at the same time, philosophy is one of the few disciplines that allow us to ask all the BIG questions, like "What is truth?", "Why are we here?" and "How much wood would a woodchuck chuck if a woodchuck could chuck wood?"
1) It's what we agree it is
2) Because it's more fun than not being here
3) A woodchuck would chuck all the wood he could chuck if a woodchuck could chuck wood
Regarding epistemology GSquared, what if we're all wrong? I like Nietzsche's take on it better:
The falseness of an opinion is not, for us, any objection to it. The question is how far it is life furthering, life preserving, species preserving and perhaps species creating.
Even if he's wrong, it's at least thought-provoking. Also, note that this definition includes the idea that the truth evolves over time, subject to natural selection just as we ourselves and all other life forms are.
The greatest enemy of knowledge is not ignorance, it is the illusion of knowledge. - Stephen Hawking
June 2, 2011 at 2:04 pm
"Why are we here?"
"To help others."
"Then what are the others here for?"
______________________________________________________________________________
How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics.
June 2, 2011 at 4:17 pm
mtillman-921105 (6/2/2011)
....Regarding epistemology GSquared, what if we're all wrong? I like Nietzsche's take on it better:
The falseness of an opinion is not, for us, any objection to it. The question is how far it is life furthering, life preserving, species preserving and perhaps species creating.
Even if he's wrong, it's at least thought-provoking. Also, note that this definition includes the idea that the truth evolves over time, subject to natural selection just as we ourselves and all other life forms are.
Honestly, the best definition of Truth that I know of is: Does it work?
A datum is as valuable as it can be compared to other data in such as way as to allow predictable results to be achieved, and to the magnitude that it affects survival along the lines of self, family, children, groups, species, biosphere, material universe, spiritual universe, infinity/God. Survival can be measured in both quantity and quality. And, all values are subjective.
That's a more embracive evaluation of the valuation of data. It is, of course, recursive, in that the statement applies to itself just as much as to anything else.
Another thing to keep in mind is that Right/Wrong is best viewed as a gradient scale, not as a binary evaluation. Right and Wrong are also all subjective. What's "Right" for the bacterium may not be "Right" for the host, and vice-versa. Things can be "more right" than other things, or "more wrong", et al.
There's a LOT more to this material, all of it valuable to lesser or greater extents.
- Gus "GSquared", RSVP, OODA, MAP, NMVP, FAQ, SAT, SQL, DNA, RNA, UOI, IOU, AM, PM, AD, BC, BCE, USA, UN, CF, ROFL, LOL, ETC
Property of The Thread
"Nobody knows the age of the human race, but everyone agrees it's old enough to know better." - Anon
Viewing 15 posts - 1 through 15 (of 158 total)
You must be logged in to reply to this topic. Login to reply