- #1
cscott
- 782
- 1
Why does my calculator tell me -1/(0^2) = -infinity. How is this different from 1/0?
That makes sense. The calculator is probably computing the limit of those functions as they go to 0, which is infinity for even functions and undefined for odd.Hurkyl said:Incidnetally, the function
-1/x²
does have a continuous extension to x=0 in the extended real numbers. Whereas
-1/x
does not.
The mathematical concept of division by zero is undefined, meaning that it has no definite value. In this case, -1 divided by 0 squared results in a number that is infinitely small, but not equal to zero. This is why it is represented as -Infinity.
1 divided by 0 is also undefined, but it is represented as Infinity because it is a number that is infinitely large. This is because as the denominator approaches 0, the quotient approaches infinity.
No, it cannot be simplified to a different value. As mentioned before, division by zero is undefined, and the result of -Infinity is the most accurate representation.
The concept of division by zero is relevant in mathematical proofs and equations, as it can lead to contradictions and inconsistencies. It is also used in fields such as calculus and complex analysis to understand the behavior of functions near points where the denominator is equal to zero.
No, it cannot. The result will always be -Infinity, regardless of the value of -1. This is because any number divided by a number that is infinitely small will result in a number that is infinitely large.