Question: Why Is Infinity * 0 Indeterminate?

What is the LN of 0?

The real natural logarithm function ln(x) is defined only for x>0.

So the natural logarithm of zero is undefined..

What is infinity divided 0?

Similarly, any expression of the form a/0, with a ≠ 0 (including a = +∞ and a = −∞), is not an indeterminate form since a quotient giving rise to such an expression will always diverge. Originally Answered: What if infinity is divided by zero? Infinity divided by zero is undefined.

Why is 1 Infinity undefined?

Infinity is a concept, not a number; therefore, the expression 1/infinity is actually undefined. In mathematics, a limit of a function occurs when x gets larger and larger as it approaches infinity, and 1/x gets smaller and smaller as it approaches zero.

What is Ln infinity?

1 Answer. Amory W. The answer is ∞ . The natural log function is strictly increasing, therefore it is always growing albeit slowly.

Can you do infinity times infinity?

11 Answers. The problem is that the laws of addition and multiplication you are using hold for natural numbers, but infinity is not a natural number, so these laws do not apply. If they did, you could use a similar argument that multiplying anything by infinity, no matter how small, gives infinity, thus ∞×0=∞.

Is Infinity * 0 indeterminate?

When you divide infinity by 0, we don’t know whether you’re dividing by a positive or negative number, so we can’t determine if the result is infinity or negative infinity. That’s why it’s indeterminate.

What is the value of 0 * infinity?

This also points to the fact that infinity is not a number , rather a concept and hence multiplication does not hold any meaning in this case, as proved above. Remember that although infinity is a concept, a number can tend to infinity. So 0*inf is undefined.

Can zero be divided by zero?

They say zero divided by anything is zero. However, some say anything divided by zero is undefined, since 4/0 and 5/0 are and so on. … If 0/0 is 1, then 1 times 0 is , so it is correct. If 0/0 is 0, then 0 times 0 is 0, so it is also correct.

How do you know if a limit is indeterminate?

So, L’Hospital’s Rule tells us that if we have an indeterminate form 0/0 or ∞/∞ all we need to do is differentiate the numerator and differentiate the denominator and then take the limit.

Why is infinity times zero indeterminate?

Zero is so small that it makes everyone vanish, but infinite is so huge that it makes everyone infinite after multiplication. In particular, infinity is the same thing as “1 over 0”, so “zero times infinity” is the same thing as “zero over zero”, which is an indeterminate form.

Can you multiply infinity by zero?

In actuality, when any number (including zero) is multiplied with infinity, then the results are always undefined. Therefore, zero times infinity is undefined. So, zero times infinity is an undefined real number. This is the definition of undefined.

Is 1 to the infinity indeterminate?

Forms that are not Indeterminate Quotient: The fractions 0 ∞ \frac0{\infty} ∞0​ and 1 ∞ \frac1{\infty} ∞1​ are not indeterminate; the limit is 0 0 0. The fractions 1 0 \frac10 01​ and ∞ 0 \frac{\infty}0 0∞​ are not indeterminate. If the denominator is positive, the limit is ∞ \infty ∞.

Why is the power of infinity indeterminate?

For example, limn→∞(1+1n)n=e≈2.718281828459045. limn→∞(1+1n)√n=0, so a limit of the form (1) always has to be evaluated on its own merits; the limits of f and g don’t by themselves determine its value.

Is infinity times 2 bigger than infinity?

Infinity can never be smaller or larger then infinity. Infinity is not a number. It is a size, a manyness. Georg Cantor proved that there are 2 and only 2 sizes of infinity.

What is 2 to the power infinity?

Although, (something)^infinity=infinity in general. And here we can prove it as follows.. Here look the infinity means a very very large quantity that means unreachable quantity so simply, {something}^infinity= a very very large quantity(unreachable) that means infinity. So clearly 2^infinity=infinity.