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Thread: What if 0 didn't exist?

  1. #1 What if 0 didn't exist? 
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    I read that it wasn't used in the past though from what I understand it helps a great deal to be able to use 0. What if it simply didn't exist? I'm no mathematician but i'm sure it's helped us create many equations, Do you think it might be possible to have advanced mathematics without 0?


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    To put it in simple terms, no. Modern mathematics would not be possible without "0". There are numerous reasons, but I'll just go with one small example: A mathematical ring, by definition requires an identity element in its addition operation. This means that there must exist some object 'a', such that a + b = b. When this operation is performed over any numerical ring, that object must be 0. Thus, without 0 you have no rings, and without rings you have no fields, and without fields, you kill a lot of linear algebra and discrete maths.

    I hope this answers your question, feel free to ask for more clarification, I'm kind of in a hurry right now.


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    All of mathematics is built upon a core of axioms. Several of these would become invalidated by a lack of zero, so the subject itself would have no "ground" upon which to stand.
    "Simplicity of character is no hindrance to the subtlety of intellect." -John Morley
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    Quote Originally Posted by MarPlo View Post
    Hy,
    I think that like in the universe exist void, in mathematics should to exist 0.
    My math teacher, who was formerly the head of the math department at a large university, used the symbol "sigma" to substitute for zero. Sigma is a very small number compared to the numbers normally used. The sigmas of equations can also be the errors in the calculations or the noises that inevitably creep into real world situations.

    As to "infinity", Planck said that it is simply a very large number, which is quite different from the hypothetical infinity of today's physics. Planck did quite well with it, and his radiation equation has withstood the test of time.
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    Quote Originally Posted by sharpsword View Post
    Quote Originally Posted by MarPlo View Post
    Hy,
    I think that like in the universe exist void, in mathematics should to exist 0.
    My math teacher, who was formerly the head of the math department at a large university, used the symbol "sigma" to substitute for zero. Sigma is a very small number compared to the numbers normally used. The sigmas of equations can also be the errors in the calculations or the noises that inevitably creep into real world situations.
    Makes no sense. Zero isn't a very small number. It's zero.

    As to "infinity", Planck said that it is simply a very large number, which is quite different from the hypothetical infinity of today's physics. Planck did quite well with it, and his radiation equation has withstood the test of time.
    What do you mean by "hypothetical infinity of today's physics"? How is it different than Planck's idea of infinity?
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  7. #6  
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    If you don't believe that zero exists you would agree my statement "Every guys on earth has a good looking face.". Zero represents the condition of the absence of existence.
    "Imagination is more important than knowledge" - Albert-Enstein
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    Quote Originally Posted by Harold14370 View Post
    Quote Originally Posted by sharpsword View Post
    Quote Originally Posted by MarPlo View Post
    Hy,
    I think that like in the universe exist void, in mathematics should to exist 0.
    My math teacher, who was formerly the head of the math department at a large university, used the symbol "sigma" to substitute for zero. Sigma is a very small number compared to the numbers normally used. The sigmas of equations can also be the errors in the calculations or the noises that inevitably creep into real world situations.
    Makes no sense. Zero isn't a very small number. It's zero.

    As to "infinity", Planck said that it is simply a very large number, which is quite different from the hypothetical infinity of today's physics. Planck did quite well with it, and his radiation equation has withstood the test of time.
    What do you mean by "hypothetical infinity of today's physics"? How is it different than Planck's idea of infinity?
    Planck derived his famous radiation equation without relying on abstract equations. The use of "infinity" is, however replete in today's physics, is it not? In the Laplace transform, the concept of "poles" and "zeroes" are utilized with excellent results. However, in the Laplace equation, it take infinite time to have an infinite result. The same result could be obtained by using "sigma" a very small number.
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  9. #8  
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    I heard that a small epsilon was the designation for an infinitesimal.
    I was some of the mud that got to sit up and look around.
    Lucky me. Lucky mud.
    -Kurt Vonnegut Jr.-
    Cat's Cradle.
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    Quote Originally Posted by GiantEvil View Post
    I heard that a small epsilon was the designation for an infinitesimal.
    to be honest i have never agreed with the current science that tend to use "infinity".
    There is no infinity.... we just couldn't reach the level of technology to go beyond our capability now.
    "Imagination is more important than knowledge" - Albert-Enstein
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    Quote Originally Posted by Kiwisoft View Post
    Quote Originally Posted by GiantEvil View Post
    I heard that a small epsilon was the designation for an infinitesimal.
    to be honest i have never agreed with the current science that tend to use "infinity".
    There is no infinity.... we just couldn't reach the level of technology to go beyond our capability now.
    Why do you say that current science tends to use infinity?
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    Quote Originally Posted by Harold14370 View Post
    Quote Originally Posted by Kiwisoft View Post
    Quote Originally Posted by GiantEvil View Post
    I heard that a small epsilon was the designation for an infinitesimal.
    to be honest i have never agreed with the current science that tend to use "infinity".
    There is no infinity.... we just couldn't reach the level of technology to go beyond our capability now.
    Why do you say that current science tends to use infinity?
    In astronomy, if i am not mistaken, people always says that our universe is infinity..... the size and height can not be meazured.... so if the pupil in the class ask the teacher "How big is the universe" the teacher always says "infinity" (too big to be measured)
    "Imagination is more important than knowledge" - Albert-Enstein
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    Gee Kiwisoft, did you notice I said "infinitesimal", not "infinite"?
    Infinitesimal - Wikipedia, the free encyclopedia
    I was some of the mud that got to sit up and look around.
    Lucky me. Lucky mud.
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    Quote Originally Posted by Kiwisoft View Post
    In astronomy, if i am not mistaken, people always says that our universe is infinity..... the size and height can not be meazured.... so if the pupil in the class ask the teacher "How big is the universe" the teacher always says "infinity" (too big to be measured)
    So by "current science" you mean a science teacher you once had who said the universe is infinite?
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    Quote Originally Posted by GiantEvil View Post
    Gee Kiwisoft, did you notice I said "infinitesimal", not "infinite"?
    Infinitesimal - Wikipedia, the free encyclopedia
    i thought they are the same. He...he... i apologize for that
    "Imagination is more important than knowledge" - Albert-Enstein
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    Quote Originally Posted by Harold14370 View Post
    Quote Originally Posted by Kiwisoft View Post
    In astronomy, if i am not mistaken, people always says that our universe is infinity..... the size and height can not be meazured.... so if the pupil in the class ask the teacher "How big is the universe" the teacher always says "infinity" (too big to be measured)
    So by "current science" you mean a science teacher you once had who said the universe is infinite?
    should i say "main stream" science ? and what the scientist says today ?
    Last edited by Kiwisoft; September 3rd, 2011 at 06:30 PM.
    "Imagination is more important than knowledge" - Albert-Enstein
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    Quote Originally Posted by Kiwisoft View Post
    should i say "main stream" science ? and what the scientist says today ?
    No it doesn't matter what you call it. Yes, you do need to say specifically which scientist you are referring to, and specifically what they say, with which you disagree.
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    Quote Originally Posted by Harold14370 View Post
    Quote Originally Posted by sharpsword View Post
    Quote Originally Posted by MarPlo View Post
    Hy,
    I think that like in the universe exist void, in mathematics should to exist 0.
    My math teacher, who was formerly the head of the math department at a large university, used the symbol "sigma" to substitute for zero. Sigma is a very small number compared to the numbers normally used. The sigmas of equations can also be the errors in the calculations or the noises that inevitably creep into real world situations.
    Makes no sense. Zero isn't a very small number. It's zero.

    As to "infinity", Planck said that it is simply a very large number, which is quite different from the hypothetical infinity of today's physics. Planck did quite well with it, and his radiation equation has withstood the test of time.
    What do you mean by "hypothetical infinity of today's physics"? How is it different than Planck's idea of infinity?
    I imagine that hypothetical infinity is any number that is so great that it is unimaginable. Take any number and continue doubling it until you reach infinity.
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    Quote Originally Posted by sharpsword View Post
    I imagine that hypothetical infinity is any number that is so great that it is unimaginable. Take any number and continue doubling it until you reach infinity.
    Is it hypothetical just because you cannot imagine it? What is the difference with Planck's idea of infinity, of which you seem to approve? Planck's radiation formula has an exponential in it. This is a number that gets smaller and smaller but never reaches zero at any finite value.
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    The concept of "0" exists in nature, as in when one has no money in their pocket - or account. At some point, the most primitive plains walking, tree climbing humans had to be hungry and realized they had "0" sheep carcases, "0" nuts and berries and were out of food. I doubt they had a symbol for it, but they had the idea.

    If I'm recalling correctly, Roman numerals did not have a symbol for "0". I don't think the Egyptians, Greeks, Babylonians or Chaldeans prior had such a symbol, either. Much of their mathematics was limited due to this. Since most of their mathematics was practical in nature - like figuring acreage owned by a farmer or height of a building - it didn't make much practical difference. The symbol "0" is commonly attributed to 'Arabic' - actually Indian/Hindi - numbers, introduced to the Western world - Europe - in the latter part of the First Millennium.

    If we didn't have "0", we'd have to invent it.
    The universe is a real place. However, you can't see it, you have to imagine it. Like it or not, God designed, built and sustains the Universe. Deal with it.
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    What if...
    I like to think out loud, typing.
    Let's see... set the number of zeros to zero...
    Start again... decrease the number of zeros from one to...
    Anyone know Kurt Godel's phone number?
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    Quote Originally Posted by Three26 View Post
    I read that it wasn't used in the past though from what I understand it helps a great deal to be able to use 0. What if it simply didn't exist? I'm no mathematician but i'm sure it's helped us create many equations, Do you think it might be possible to have advanced mathematics without 0?
    Very funny question, "what if zero didn't exist". I mean thihnk about it, "zero" is a concept of non-existence, and here the question is being asked "what if zero didn't exist" (gee that took me a while).

    Very clever. So what you're suggesting is that we take the concept of "zero" too seriously, or have yet to fully understand how to define zero in purely imaginary terms?
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  23. #22  
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    Quote Originally Posted by theQuestIsNotOver View Post
    Very funny question, "what if zero didn't exist". I mean thihnk about it, "zero" is a concept of non-existence,...
    The answer needs be more articulate, we must distiguish between the word "zero" and the math symbol "0" which is read, pronounced "zero, nought or nil"

    a) the word does not refer to the concept of non-existence, the philosophical "nothing" made world-famous by Sartre's "Being and nothingness"
    it is related to the linguistic concept of negation, expressed by "no, not" , and other substitutes like "small amount", "empty" "false" etc
    on the table/tray are zero books => the table/ tray is empty
    you have zero chances => you do not have a chance

    b) symbol 0 is sometimes, erroneously, considered a number. Pythagoras and other scientists believed (rightly, I'd say) that even 1 is not a number.
    0 is just a sign, chiefly a marker for empty space and, as such, not necessary. Quipus use knots instead of numbers, and no knot is zero.
    So if we dropped 0 nothing much would happen, there might be some confusion if we were not meticulous

    equations would look [ 80 -4(5*4) = ], number 2408 would look [24 8], we might use any marker, like 24_8
    Position itself would be useless if we used colours, so 48 woud be 48 or 84

    infinite, infinity is sometimes (wrongly) considered a number and related to zero or infinitesimal in math, for details see wiki:infinity
    as a word is, like nothing(ness) literally, semantically meaning-less, that is a word signifier without a signified (meaning)
    (ancient wisemen were wise and thought "infinitum in actum non datur",in math, alas, they consider not only infinite, but countable, uncountable infinite and transfinite, but this is foreign to OP)
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    Quote Originally Posted by ray View Post
    Quote Originally Posted by theQuestIsNotOver View Post
    Very funny question, "what if zero didn't exist". I mean thihnk about it, "zero" is a concept of non-existence,...
    The answer needs be more articulate, we must distiguish between the word "zero" and the math symbol "0" which is read, pronounced "zero, nought or nil"

    a) the word does not refer to the concept of non-existence, the philosophical "nothing" made world-famous by Sartre's "Being and nothingness"
    it is related to the linguistic concept of negation, expressed by "no, not" , and other substitutes like "small amount", "empty" "false" etc
    on the table/tray are zero books => the table/ tray is empty
    you have zero chances => you do not have a chance

    b) symbol 0 is sometimes, erroneously, considered a number. Pythagoras and other scientists believed (rightly, I'd say) that even 1 is not a number.
    0 is just a sign, chiefly a marker for empty space and, as such, not necessary. Quipus use knots instead of numbers, and no knot is zero.
    So if we dropped 0 nothing much would happen, there might be some confusion if we were not meticulous

    equations would look [ 80 -4(5*4) = ], number 2408 would look [24 8], we might use any marker, like 24_8
    Position itself would be useless if we used colours, so 48 woud be 48 or 84

    infinite, infinity is sometimes (wrongly) considered a number and related to zero or infinitesimal in math, for details see wiki:infinity
    as a word is, like nothing(ness) literally, semantically meaning-less, that is a word signifier without a signified (meaning)
    (ancient wisemen were wise and thought "infinitum in actum non datur",in math, alas, they consider not only infinite, but countable, uncountable infinite and transfinite, but this is foreign to OP)

    However way you want to think about it, or however articulate you want to be, the concept of "0" can be subdivided or utilised in any format. But it's representation of being "naught" still stands true to whatever context it is used within. We as mathematicians have adopted the symbol "0" because ultimately in a decimal system it makes sense, it's efficient, it creates an efficiency of subdividing symbols, especially numerical symbols.

    "Zero" on it's own, without any other context, like "0" on it's own, without any other context, are symbols both verbal and numerical that without any other context mean the same thing, don't you think?
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    The standard definition/construction of the natural numbers 0, 1, ..... which are the basis of all other number systems,
    is due to von Neumann.

    He defined the first (base) number zero (denoted by the symbol '0') to be the empty set (denoted by the Danish letter , which happens to be here on my Nordic keyboard).

    is the mathematical representation of the concept 'nothing'.

    But 'nothing' is an important concept in maths and in physics, and we need to have a representation for it, because
    so much else depends on it, as has been stated before (by Sploit and Cellar Door).
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    Wow............what a question ?

    • What if 0 didn't exist?

    I think without zero today math and even computer field can't move a single step .I am not a great mathmatician but it's true .
    But here lots of people have given best answers .The best thing about this question is that it is ver interesting and intelligent question and so it had created such a great discussions among scholars .
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    Creating such Math equations at the computer,
    the hand write of the Zero interpretation makes much more sense.
    Since at the computer you can be able to direct experiment and apply the zero effect.

    Zero is the count for nothing. In math you cannot answer "nothing" but you do "zero".
    Nothing can be a result about anything,zero than is a math result.
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    If zero didn't exist, it would have to be invented.
    Strange likes this.
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