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Oh, what a lovely question! When you divide infinity by infinity, you're entering a realm of endless possibilities and wonder. In mathematics, this expression is considered indeterminate because infinity is not a fixed number. Embrace the beauty of the unknown and continue exploring the infinite canvas of mathematics with joy and curiosity.
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Rene
Professor
CoachFirst off, infinity is not a number in conventional mathematics.
In Calculus, you can work with infinity through the language of limits. It is important to note that when we use the shorthand:
∞/∞
What we are REALLY saying is "the limit of a function which diverges to infinity divided by the limit of a function which diverges to infinity". We are not actually saying "infinity divided by infinity".
Now that THAT is out of the way, we can get to the answer.
∞/∞ is of indeterminate form, meaning that the division could converge to 0, it could converge to 1, it could converge to an arbitrary constant, or it could diverge to infinity.
In order to figure out which of these cases is true, you need to apply L'Hospital's rule, by taking the derivative of the numerator and the denominator (separately).
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What is infinity divided by 5?
Infinity divided by any finite number is infinity. Here are the rules: 1. Infinity divided by a finite number is infinite (I / f = I); 2. Any finite number divided by infinity is a number infinitesimally larger than, but never equal to, zero (f / I = 1 / I); 3. Infinity divided by infinity is one (I / I = 1), or in fact any other positive number (I / I = and so on...); 4. Infinity multiplied by zero (no infinity) is zero (I * 0 = 0); 5. Infinity divided by a positive finite number is infinity (I / +f = I); 6. Infinity divided by a negative finite number is minus infinity (I / -f = -I); 7. Infinity divided by zero is not possible; 8. Infinity plus infinity is infinity (I + I = I); 9. Zero divided by infinity (nothing divided into infinity) equals zero (0 / I = 0); 10. Infinity plus a finite number is infinity (I + f = I); 11. Infinity minus a finite number is infinity (I - f = I); but 12. Infinity minus infinity, due to the nature of infinity, can be zero, infinity, or minus infinity (I - I = -I, 0, I).
Is infinity divided by infinity equal 1?
Firstly we don't know infinity value. If you divide any number by infinity then answer will be zero. Example is divide 100/3 by infinity ( let infinity is equal to 1/0). Then answer is 100/3/1/0 you will get zero.
What does negative infinity divided by infinity squared equal?
42,100,876,9765,098.6 xx :) All real numbers, except zero and one.
Any number divided by infinity?
When any number is divided by infinity, the result approaches zero but never actually reaches it. This is because infinity is not a specific number but rather a concept representing unboundedness. Mathematically, the limit of any finite number divided by infinity as infinity approaches infinity is zero.
What is infinity divided by two?
infinity divided by any finite number is also infinity.
