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Paul Dirac
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Thanks!
axmls said:The first thing I'd say is that infinity is not a number, and so it doesn't make sense to talk about its reciprocal. In the context of calculus, we can refer to a limit, namely that [tex]\lim_{x \to \infty} \frac{1}{x} = 0[/tex]
That is to say, as x gets larger and larger, this term gets closer and closer to 0, but there is no real number called infinity that we can manipulate like a number.
Now, if I recall correctly, in the context of nonstandard analysis, you can technically call the reciprocal of infinity a "differential" (given certain assumptions), but this is avoided in standard analysis (the standard calculus that we use). When talking about infinities, we are typically dealing with limits.
See post #4Pjpic said:This may not apply, but here's a quote from Wiki:
As mentioned above, zero, the origin, requires special consideration in the circle inversion mapping. The approach is to adjoin a point at infinity designated ∞ or 1/0 .
Yes, the reciprocal of infinity is indeed zero. This is because the concept of infinity represents a quantity that is infinitely large, meaning it has no definite value. Therefore, when we take the reciprocal of infinity, we are essentially dividing by a number that has no specific value, resulting in a value of zero.
No, the reciprocal of infinity can only be zero. As mentioned before, infinity represents a quantity that is infinitely large, meaning it has no definite value. This means that any other number would not be able to accurately represent the concept of infinity.
No, the reciprocal of infinity is not undefined. It is simply equal to zero. Undefined values occur when we try to divide by zero, but in this case, we are not dividing by a specific number, but rather by a concept of infinity.
No, we cannot manipulate the value of the reciprocal of infinity. As stated before, infinity represents a quantity that is infinitely large and has no definite value. Therefore, any attempts to manipulate its reciprocal would not result in a meaningful or accurate value.
The concept of infinity is directly related to the reciprocal of infinity. As mentioned before, infinity represents a quantity that is infinitely large and has no definite value. When we take the reciprocal of infinity, we are essentially dividing by this infinitely large quantity, resulting in a value of zero.