Is the reciprocal of zero infinity? Explain? ?
- Anonymous1 decade agoFavorite Answer
THE DIVISION BY ZERO does not exist. . Undefined. Period. No other way about it.
EDIT: to expand on an answer given above, what this person is reffering to is the rational function f(x)=1/x, in which case it is as he says, but the question is the reciprocal of 0, and that is only 1/0, and this DOES NOT EXISTS.
- 5 years ago
I ve been working on Fractions in Code. They make it possible to record things like division by zero as a value, which makes things interesting.
If you calculate how many pieces of one cake can give to two people, you will get half each. 1 cake / 2 people. For one person, it s one cake each - 1 cake / 1 person. It gets interesting when you have half a person. You would have 1 cake / 0.5 people. We can t represent a fraction like that - so we multiply both sides by the minimum value you would need to make the denominator (bottom number) a whole number, and it becomes 2 / 1. As you move towards 0 people, the number of cakes increases. 0.25 people get 4 cakes each. 1 / 0.25 or 4 / 1. Extrapolating, we get 1 / 0 equals infinity.
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Zero can be represented as 0 / n. To get the reciprocal of a fraction, we simply flip it on its head - so we get n / 0 which is (according to the cake example above) infinity.
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Infinity is not undefined. "Undefined" or "Does Not Exist" or "NaN" (Not a Number) are error conditions for number systems that do not support such difficult calculations. IEEE Floating Point Standards define PositiveInfinity and NegativeInfinity, but declare that PositiveInfinity * 0 = NaN. We can simplify matters by declaring that *any* number multiplied by zero *must be* zero, and with Fractions, we can support that.
If you really want to twist your mellon, think about this: What is the value of 0 / 0? Answer: If we draw out a graph of x / y, we find that the value increases the closer y gets to zero. But at the same time, it decreases the closer x gets to zero. Since 1 / y tends towards +infinity as y approaches zero, and we know 1 / 0 = infinity, we could say that 2 / 0 = 2 * infinity. Similarly 0.5 / 0 = 0.5 * infinity, and so forth, and 0 / 0 = 0 * infinity which equals zero.
- 4 years ago
When you divide by zero, either it's an error, or there are circumstances where it looks like division by zero, but there is some calculus limit involved. Division by zero is undefined. But in calculus, it may have some particular value. It's probably large, unless the numerator is also large. In any case, if you get a real value, then it's not remotely the same as infinity. The same is true for infinity. In some limit, 1 / infinity may approach zero. But it also may not. It depends on the details of the infinity you're talking about. Let's say that you are building a calculator for sale to the public. 1/0 isn't infinity. It's "not a number". That's because, in general, you haven't the foggiest clue what kind of zero it is. Likewise, you have to assume that you can't do anything with "not a number". But now let's say your calculator can do symbolic math. Let's say it handles calculus. Now things are a little trickier.
- 5 years ago
theoretically zero and infinity are nearly opposites. Zero is an absolute, but it is an absolute value of nothingness. Infinity, by its definition must always be something, so it can never be nothing, but it is not an absolute. The issue is that we do not have a symbol, or function, or operator, that is an absolute value for the upper limits of the number scale since we do not know where it ends, or we assume that is goes on forever. The question I have to ask is, "Does zero really exist? Given the fact that it represents nothing, it can't be quantified, it has no reciprocal, and it does not work like any other real number within the confines of established math?".
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- JanetLv 44 years ago
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The question is very deep and philosophical, and I tend to avoid getting to deep into philosophy on account of personal limitation and the fact that Ithink it could drive some people crazy. I think that the number 0 may be a lie. After all, it holds a place in any number system of which I am familiar, most notably the decimal and binary systems. It could not hold a place if it did not exist. Also, it has an effect, which something that is null, or a nonentity could not do. For example, 5 to the power of 1 is 5. It stays the same. however, please note that 5 to the power of 0, or any number to the power of 0 ends up as being 1. Can nothing have an influence other than a completely passive one. I think that infinity as an entity can either expand or shrink, so the other numbers, both rational and irrational may exist. I am about to leave this argument. I keep being reminded of the news account about the math professor in England who shot his wife because she had interrupted his trian of thought. I thnk people should be careful of how much they attempt to draw abstractions and analogies, especially from one field to another.
- 1 decade ago
the reciprocal of zero is undefined. you can never divide by zero. however, if you apply limits, the reciprocal of zero from the left is negative infinity while the reciprocal of zero from the right is positive infinity. this will look like 1/0+ or 1/0-, and any nonzero divided by x such that x approaches zero is infinity.Source(s): school
- ?Lv 61 decade ago
Nope, it's undefined - that is to say, there is no such creature. However, the limit as x approaches 0 from the right, of 1/x, is infinity and the limit as x approaches 0 from the left, of 1/x, is -infinity.
Look at the graph of y=1/x . Hopefully this graph is commited to your memory, but if it isn't , use a TI-83 calculator to graph it.
The graph has no corresponding y value when x=0 (there is a vertical asymptote there) so 1/0 does not exist. However we can see that as x gets closer to 0 from the left the y value gets smaller and smaller and drops to -infinity. Similarly, as x->0 from the right, y-> infinity.
- lydia eLv 41 decade ago
eg. 0/ 1 = 0/100 = 0/100000000 = ZERO
But the reciprocal:
1/0 = 100/0 = 100000000/0 = DNE = undefined = infinity
DNE = does not exits.Source(s): UTx Grad
- TitoBobLv 71 decade ago
From a practical standpoint, you are asking how many "nothings" are there in a "something", i.e., like 5/0. You could have as many as you want, so the value is undefined, although you could think of it as infinity. In other words, there are an infinite number of nothings in any non-zero number.Source(s): Retired math teacher