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Math question

Discussion in 'The OT' started by dorfd1, Mar 18, 2009.

  1. Mike Bertelson

    Mike Bertelson 6EQUJ5 WOW! Staff Member Super Moderator DBSTalk Club

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    1/3=0.3(repeating) is also a fact.

    It isn't a philosophical argument. There are no assumptions to be made.

    It is a concrete mathematical certainty.

    I do not understand how something we all learned in grade school should be so controversial. :shrug:

    http://en.wikipedia.org/wiki/Recurring_decimal
    http://en.wikipedia.org/wiki/0.999
    http://mathforum.org/library/drmath/view/55845.html
    http://math.hws.edu/~mitchell/Math331S09/Day01.pdf
    http://mathworld.wolfram.com/RepeatingDecimal.html

    Google will show many other examples of this very discussion. In every single one of them 1/3=0.3(repeating).

    Mike
     
  2. spartanstew

    spartanstew Dry as a bone

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    Grade school is also the place where many learned of Santa Claus and the Easter Bunny. If people stop questioning, they stop learning.

    That's the difference between a mathematician and a philosopher (generally speaking).

    1/3 = .333~ is very similar to Thompsons Lamp paradox. A philosopher will examine the problem from all angles and may eventually state that there's no way to determine the state of the lamp after two minutes, because it will never reach 2 minutes (much like .333~ will never reach 1/3). A mathematician will state a formula and tell you it's so (and expect everyone he teaches it to to believe him- grade school or not), since even though the clicking of the lamp will never stop (before 2 minutes), it gets close enough.
     
  3. James Long

    James Long Ready for Uplink! Staff Member Super Moderator DBSTalk Club

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    What it boils down to is the precision of the system.

    Cut a pie into three parts and you may think you have thirds of the whole, but you're ignoring what is left on the knife. It comes down to precision.
    PI is not 3.141592 etc ... the number we assign (regardless of digits) is just as close as we can get. Saying 1/3 = 0.333(repeating) is a similar shortcut. 0.333(repeating) does not really equal 1/3 - but we have ACCEPTED in our society that it does.

    When the aliens check our work I hope they agree --- otherwise there will be some error in the communication. :)
     
  4. Mike Bertelson

    Mike Bertelson 6EQUJ5 WOW! Staff Member Super Moderator DBSTalk Club

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    Santa Claus and the Easter Bunny? I'm sorry but that was lame. I didn't have to wait until I got into school to believe in Santa. I learned about Santa from my mom. :D

    Thompson's Lamp, however, I like as an analogy. :D

    I’m a firm believer in questioning.

    However, is it reasonable to question 2+2=4?

    Because that is what we are doing here. No, really...read on. :D

    Pie? Really? We’ve got pie left on the knife? Ok, that one made me chuckle into my Cheerios. :lol:

    Ooooookaaaay, I commission a project to have the three wedges to be machined from billet Unobtainium.

    Each is machined by computer and measured by a scanning tunneling electron microscope to determine that each wedge contains exactly the same number of Unobtainium atoms. The scanning tunneling electron microscope is calibrated by NASA engineers to be…..well you know the rest. :D

    The three wedges, when combined, create a single Unobtainium pie. :rolleyes: :lol:

    Everyone seems to be forgetting what the repeating part represents.

    In this case repeating means to infinity. It doesn’t mean to infinity but let’s ponder the implications of the impossibility of having infinitely anything. :grin:

    Mathematically speaking, it is repeating to infinity regardless of our ability to write 3 infinity times.

    But, for you philosophy majors out there, I’ll concede that zero point three repeating is a mathematical representation just as π or e. ;)

    However, any inaccuracies are such that they would be infinitely small. :grin: Get it....infinitely small...:lol:...I slay me....:lol:

    All I’m saying is that just because our minds can’t deal with infinity doesn’t negate the fact that converting one third to a decimal gets you an infinite sequence of threes to the right of the decimal place. In that sense, 0.3 repeating is exactly equal to 1/3 not because we accept it to be but because it actually is. :D

    This has been a really fun discussion and I’m serious about that. I really enjoy this kind of debate. :)

    Mike
     
  5. 4HiMarks

    4HiMarks Hall Of Fame

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    It's getting more fun. I'm glad you can take some of the heat I was getting.

    In terms of "dealing with infinity", speak for yourself. My mind can handle it quite well, thank you.

    I was just getting ready to bring up learing the decimal equivalent of 1/3 in grade school myself. I agree with you completely. People seem to have no trouble understanding that the combination of "1", "/", and "3" represents the abstract mathematical quantity we call "one third" but don't seem to grasp that the combination of ".", "3", and "...(repeating indefinitely)" represents the same quantity even though we were taught this in, what, 5th grade? Shortly after learning fractions, we learn how to convert them to decimals.

    .333...(repeating indefinitely) is equal to 1/3 exactly. The same as
    .5000...(repeating indefinately) is equal to 1/2 exactly (and so is .4999...(repeating indefinitely)). It matters not whether you can write down infinitely many 3s. You can write "repeat indefinitely".
     
  6. spartanstew

    spartanstew Dry as a bone

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    Thank you. Exactly correct.

    For the record, I do believe 1/3 = .333.... from a mathematical standpoint, but not from a philosophical standpoint. It's a very thin distinction and caused all kinds of issues with professors as I was studying both. They all thought I just liked to be difficult and argue (which of course is true also).

    I just always find it somewhat amusing that discussions with Mathematicians always end up the same way. "how can it not be true, it's in all the books" or "what do you mean, we learned that when we were in 5th grade". I try to rarely rely on what is written in outdated textbooks or what an Elementary school teacher thinks is fact. It's like if it doesn't fit into their box of logic, their head will explode. Of course, discussions with Philosophers always end up the same way too: they just want to get high and think about it some more. So, you can't really win.
     
  7. FHSPSU67

    FHSPSU67 CE'er & Retired Engineer DBSTalk Club

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    Anyone care to discuss (argue) the merits of any number being divided by zero being "undefined" as taught by a lot of schools today, or my prefernce that it is "infinity". I've always felt that I could work with "infinity" in an expression, but how do you work with "not defined"?
     
  8. dorfd1

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  9. Mike Bertelson

    Mike Bertelson 6EQUJ5 WOW! Staff Member Super Moderator DBSTalk Club

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  10. dorfd1

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  11. Mike Bertelson

    Mike Bertelson 6EQUJ5 WOW! Staff Member Super Moderator DBSTalk Club

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    Well....Ok then.....:scratchin

    It must be true if YouTube says so....:rolleyes:
     
  12. 4HiMarks

    4HiMarks Hall Of Fame

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    The problem is that as far as "working with it in an expression" goes, infinity is undefined. To really discuss why, we'd have to get into limits, convergence, uniform convergence, and a whole bunch of graduate-level anaylsis that I haven't looked at in almost 20 years, and was never that good at to begin with.

    Transfinite arithmetic is very, very tricky, and counterintuitive. If you allow 1/0 = infinity, then what is infinity/0 or 0/0? Or what of infinity times 0? There are many such expressions. L'Hopital's Rule tells how to deal with many of them when they occur in functions, but as static "numbers" they have no meaning. I.e. they are undefined.

    Which infinity is greater, just the even numbers or all numbers, both even and odd? (The answer may surprise you.)
     
  13. dorfd1

    dorfd1 Icon

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    both even and odd infinity is greater
     
  14. 4HiMarks

    4HiMarks Hall Of Fame

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    Nope. They are the same. (Told you the answer would surprise you.) Every even number is two times exactly one of "all the numbers".

    2 -> 1
    4 -> 2
    6 -> 3
    8 -> 4
    ...

    In fact, that is one of the definitions of an infinite set - it can be placed in one-to-one correspondence with a proper subset of itself.
     
  15. FHSPSU67

    FHSPSU67 CE'er & Retired Engineer DBSTalk Club

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    It's been a long time since I worked with L'Hopital's Rule, but I seem to remember it's proof depending on 1/0 equalling infinity.
     
  16. James Long

    James Long Ready for Uplink! Staff Member Super Moderator DBSTalk Club

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    Exactly ... if you assume your proof found on the internet is absolute and unquestionable truth then you must allow for other people's proof on the internet to also be absolute and unquestionable. Both sources are on the internet.

    The point I'm trying to get to is that what you are claiming as an absolute truth because it is what it is NOT because it is generally accepted by those who say what it is.

    I seem to remember a planet named Pluto when I was growing up. If you're saying that 1/3 = 0.3333(repeating) because Ms. Fegley told me so in 5th grade (or was it Mr Meacham in 6th grade?) then those teachers owe me an apology for what they said about Pluto. If people are going to say WITH CERTAINTY that what is generally accepted "IS" a fact then they open themselves up to ridicule when the "facts" change.

    So I hope that you will agree with me that it is commonly accepted that 1/3 = 0.3333(repeating) and walk away from the "it is a fact" language. As stated before, the aliens may not agree with OUR interpretation of facts.
     
  17. James Long

    James Long Ready for Uplink! Staff Member Super Moderator DBSTalk Club

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    I'd prefer to call it impossible than undefined, but it is generally accepted as "undefined" so I'll go along with it --- this time. :D

    The logic of one divided into three is one being split into three equal parts.
    The logic of one divided into two is one being split into two equal parts.
    The logic of one divided into one is one being split into one equal parts.
    All three are logically possible (ignoring the loss in the cutting process :)).

    The logic of one divided by zero is one being split into no parts.
    Can you split something into nothing? Not really. It is more of a subtraction than a division problem. "I have one and now I have no parts." If you have no parts then perhaps the true answer should be x/0 = 0 but it doesn't deal with the remainder.
     
  18. dorfd1

    dorfd1 Icon

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    unless you or someonelse can writeout out all the decimals of 1/3 then 1/3 will never equal .33 repeating it will be really close to equaling 1/3.

    no computer in the world coould display infinite decimals.
     
  19. 4HiMarks

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    How many times do we have to tell you it has nothing to do with writing or displaying anything?
     
  20. FHSPSU67

    FHSPSU67 CE'er & Retired Engineer DBSTalk Club

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    I think of it as one being divided into a smaller number than you can imagine, but when that minuscle number was multiplied by infinity, the result would be one.
    I don't think it matters which answer you work with if you truly understand the implication of each - both can be used to come up with the same correct answer. Still it can be an interesting discussion:)
     

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