In general, any real number divided by infinity is zero, and the quotient of nonzero real numbers that divide infinity is infinity.

This means that 1/ infinity=0.

The value of 1 divided by negative infinity is equal to zero.

We use the terms infinity and - infinity not as a number but to say that it gets arbitrarily large. Negative infinity means that it gets arbitrarily smaller than any number you can give. so 1 - infinity = -infinity and 1 + infinity = + infinity makes sense only when looked as in this sense.

Multiplication Property

If a number is multiplied by infinity, then the value of the product is also equal to infinity.

Hold the ALT key and type 236 on the num-lock keypad. Copy ∞ from here and paste it in your web page.

Infinity to the Power of Zero

Infinity value doesn't have a universal value. Infinity having a power equal to zero is also undefined hence it is also a type of indeterminate form.

Now this statement is most commonly (though not correctly) referred to as 1/0 = infinity and is so common in mathematics and physics that people working/studying in this field take limits to be obvious.

Infinite exponentiation means that you take 1 and multiply it by a scaler, a, infitnite number of times. Scaling by a > 1 yields greater and greater number. So, (a>1)∞=∞. Downscaling infinitly by a<1 yields 0: (a<1)∞=0.

We can say that the division by the number 0 is undefined among the set of real numbers. $\therefore$ The result of 1 divided by 0 is undefined. Note: We must remember that the value of 1 divided by 0 is infinity only in the case of limits. The word infinity signifies the length of the number.

Any number times 0 equals 0 and any number times infinity equals infinity.

Answer and Explanation: Any number divided by infinity is equal to 0. To explain why this is the case, we will make use of limits. Infinity is a concept, not an actual number, so we can't just divide a number by infinity.

Answer: Infinity to the power of zero is equal to one.

Let's understand the solution in detail. Explanation: ∞^{0} is an indeterminate form, that is, the value can't be determined exactly.

0/0 is undefined. If substituting a value into an expression gives 0/0, there is a chance that the expression has an actual finite value, but it is undefined by this method. We use limits (calculus) to determine this finite value.

Zero is just zero, it is equal to nothing. Infinity gives the sense that it keeps on going. You can take zero and add to get infinite but they are not the same in definition. Obviously 0 isn't the same number as infinity but there are interesting parallels like you pointed out.

In conventions of sign where zero is considered neither positive nor negative, 1 is the first and smallest positive integer. It is also sometimes considered the first of the infinite sequence of natural numbers, followed by 2, although by other definitions 1 is the second natural number, following 0.

Infinity is not a real number and is only used as a representation for an extremely large real number. Dividing 1 by infinity is equal to zero. In general, any real number divided by infinity is zero, and the quotient of nonzero real numbers that divide infinity is infinity.

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Infinity is a concept, not a number. We know we can approach infinity if we count higher and higher, but we can never actually reach it. As such, the expression 1/infinity is actually undefined.

Yet even this relatively modest version of infinity has many bizarre properties, including being so vast that it remains the same, no matter how big a number is added to it (including another infinity). So infinity plus one is still infinity.

Answer and Explanation: There is no number before infinity. It is possible to represent infinity minus one as a mathematical expression, but it does not actually equal anything or have any real mathematical value.

Multiplying infinity by infinity will result in infinity.

What we'll focus on in this lesson is giving precise meaning to the phrase “infinity times 2 is infinity”. Actually, what we'll show, is that “infinity type 1 times 2 is infinity type 1”.