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What is a number divided by 0?


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Is the quantity 1/infinity undefined? I mean the probability of selecting a number from the infinite series of whole numbers? Is it undefined?

 

"infinity" is not a number in some number field. So 1/infinity has no meaning.

 

One can put a probabilty measure on the set of real numbers, but not a uniform measure. For many probability measures, for instance those that are absolutely continuous with respect to Lebesgue measure, the probability of selecting any specific real number is zero.

 

Without first specifying a probability measure there is no meaning to any statement involving probability.

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Is the quantity 1/infinity undefined? I mean the probability of selecting a number from the infinite series of whole numbers? Is it undefined?

 

If you take the limit of 1/x as x approaches infinity, you get zero. f(x)=1/x for x being infinity doesn't work because infinity isn't a number.

 

If you take the limit of 1/x as x approaches 0, you don't get an answer because the left and right limits do not match. f(x)=1/x for f(0) is undefined.

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If you take the limit of 1/x as x approaches infinity, you get zero. f(x)=1/x for x being infinity doesn't work because infinity isn't a number.

 

If you take the limit of 1/x as x approaches 0, you don't get an answer because the left and right limits do not match. f(x)=1/x for f(0) is undefined.

I got you sir but is there anything wrong with my question? I mean as a calculating device human brain selects a number so is the probability of calculating a number undefined for human brain?

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We can take a look at the function as x gets bigger and bigger (taking the limit as x approaches infinity [which is just a fancy way of saying it increases without bound]). We can't, however, plug in the biggest number possible, because there is no such number.

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I got you sir but is there anything wrong with my question? I mean as a calculating device human brain selects a number so is the probability of calculating a number undefined for human brain?

Your original question appears to be asking how to construct a uniform distribution over the entire real number line. If that is the case, yes, there is something wrong with your question. A uniform distribution requires a finite interval; the probability is identically zero outside this interval. A uniform distribution with infinite extent doesn't make sense. There are probability distributions such as a Gaussian distribution that do span the entire real number line. None of these is uniform.

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Is the quantity 1/infinity undefined? I mean the probability of selecting a number from the infinite series of whole numbers? Is it undefined?

Shouldn't a number divided by 0, just stay the same? The symbol 0 means - "nothing". Not infinity - just "no-thing".

 

So suppose, for example, you say: "Divide 7 by 0". Isn't that the same as saying: "Divide 7 by nothing." Which can be put another way: "Don't divide 7 by anything". Which can be further simplified to: "Don't divide 7". So the 7 doesn't get divided - it just stays 7. That seems logical.

 

What's the supposed problem with dividing by 0 - logically it just means not dividing. Why should this cause mathematicians to get worked up?

Edited by Dekan
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Shouldn't a number divided by 0, just stay the same? ... What's the supposed problem with dividing by 0 logically it just means not dividing.

Nonsense. A number divided by 1 stays the same. Your proposed result would mean 0 = 1, a contradiction.

 

 

Why should this cause mathematicians to get worked up?

Mathematicians get worked up about contradictions because allowing contradictions would be a mathematical disaster of biblical proportions, real wrath of God type stuff. Forty years of darkness! Earthquakes, volcanoes! The dead rising from the grave! Human sacrifice, dogs and cats living together, mass hysteria!

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Simply, a number divided by zero is 0. This would be because x/2 = y and y*2 = x. So if x has y fractions, then any number put into zero fractions would cancel out the number. Bit hard to understand I think but I think it works.

Edit: I've just realised my error because that would mean that x*0 = y which is wrong. It must be either "i" (imaginary number) or infinity.

Edit 2: This shows how it must be infinity.

 

10 divided by 2 is 5.

10 divided by 1 is 10.

10 divided by 1/2 is 20.

10 divided by 1/5 is 50.

10 divided by 1/10 is 100.

10 divided by 1/100 is 1000.

10 divided by 1/1000 is 10000.

So the smaller the number it is divided by, the larger the number. If you divide by 0 then the answer is infinity.

Edited by morgsboi
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Your original question appears to be asking how to construct a uniform distribution over the entire real number line. If that is the case, yes, there is something wrong with your question. A uniform distribution requires a finite interval; the probability is identically zero outside this interval. A uniform distribution with infinite extent doesn't make sense. There are probability distributions such as a Gaussian distribution that do span the entire real number line. None of these is uniform.

 

You were absolutely correct about the answer sir. Indeed that's true!! Thank you!

 

Simply, a number divided by zero is 0. This would be because x/2 = y and y*2 = x. So if x has y fractions, then any number put into zero fractions would cancel out the number. Bit hard to understand I think but I think it works.

Edit: I've just realised my error because that would mean that x*0 = y which is wrong. It must be either "i" (imaginary number) or infinity.

 

Absolutely( for the edited part ofcourse)!!

 

 

 

10 divided by 2 is 5.

10 divided by 1 is 10.

10 divided by 1/2 is 20.

10 divided by 1/5 is 50.

10 divided by 1/10 is 100.

10 divided by 1/100 is 1000.

10 divided by 1/1000 is 10000.

So the smaller the number it is divided by, the larger the number. If you divide by 0 then the answer is infinity.

 

doesn't that possibly violate the the simple basic laws of mathematics? if x/y = z then yz =x? I mean again if we calculate the tangent of an angle 90? A ratio of infinity? At that ratio the triangle wouldn't even exist!

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doesn't that possibly violate the the simple basic laws of mathematics? if x/y = z then yz =x? I mean again if we calculate the tangent of an angle 90? A ratio of infinity? At that ratio the triangle wouldn't even exist!

But you wouldn't calculate the triangle using 0. It is a bit of a weird one. I think it must be [math]i[/math]

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What is North of the North pole?

You can't answer the question because the question is not compatible with the definition of the terms used in the question.

Since division is not defined for zero the question "what do you get when you divide by zero?" is like asking " where do you go if you travel North from the North pole?".

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I think that many learned and respected posters on this topic, may be getting confused about two simple things:

 

1. the distinction between "0" and infinity

 

2. the belief that the symbol "0" is a number - when it isn't . It's the absence of a number. Recall that the symbol was invented as a place-marker

in decimal arithmetic. It marks the absence of something . So 107 means : 1 hundred + an absence of tens + 7 units.

 

This would be clearer, if we used a different symbol as the place-marker, such as "-" . So we wrote 1-7. Then nobody would mistake "-" for a number.

 

However, we use "0" as the place-marker. The "0" looks like a number, similar to "8", or "6". And so mathematicians try to treat it as a number, when it isn't. And that's why the mathematicians get confused, and see problems and paradoxes, when really there aren't any.

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How do you conclude about the value 'i'?

Because it is a value that doesn't exist.

That isn't how it works in the slightest.

 

2. the belief that the symbol "0" is a number - when it isn't . It's the absence of a number. Recall that the symbol was invented as a place-marker[...]And so mathematicians try to treat it as a number, when it isn't. And that's why the mathematicians get confused, and see problems and paradoxes, when really there aren't any.
  • 0 is a number.
    • It doesn't fall under the range of the domain of the division function.
    • But it's still a number.

    [*]You're correct in that there are no problems or paradoxes.[*]I really doubt any mathematicians are confused by this.

Edited by the tree
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I think mister Dekan have done something wrong in his earlier argument, By using real numbers in a discrete way,

I think he should've used the set of natural numbers,

which is basically the set of all positive integers that are greater than 0

Edited by khaled
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Zero is not a number?

 

One could speculate such off the fact that it represents an empty set. However, this does not violate its status as a number.

 

By the Peano Axioms, zero is a number (specifically stated in the axioms as a natural number). And upon what is mathematics analytically founded on? Axioms.

 

Which is also the reason why one cannot truly define [math]\dfrac{1}{0}[/math]. I have to admit, it does seem as though the value is infinity. But by assuming division by zero (for the dividend is not zero itself) at all is a legitimate operation, we run into serious problems.

 

(My first real post by the way. Hi everyone )

 

EDIT: Oops. Fixed LaTex tags. Used to other forum.

Edited by Visionem Ex Illuminatio
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