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.
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.
It is known that a number subtracted from itself will result in the value 0, but there is the confusion that subtracting infinity from infinity is zero or not. But it's not so. In because infinity is not a Real Number.
The reason that the result of a division by zero is undefined is the fact that any attempt at a definition leads to a contradiction. a=r*b. r*0=a. (1) But r*0=0 for all numbers r, and so unless a=0 there is no solution of equation (1).
One to the power infinity is unknown because infinity itself is endless. Take a look at some examples of indeterminate forms. When we plug infinity into this function, we see that it takes on the indeterminate form of one to the power infinity.
1 divided by infinity:
Therefore, we consider it as zero. The larger the denominator, the closer the quotient gets to 0. So, we consider the result as 0.
In short, the multiplicative identity is the number 1, because for any other number x, 1*x = x. So, the reason that any number to the zero power is one ibecause any number to the zero power is just the product of no numbers at all, which is the multiplicative identity, 1.
One divided by infinity is not defined. Division is only defined for real numbers (with the stipulation that the denominator not be zero), and infinity is not a real number, so the result is undefined.
This means that 1/ infinity=0. Cross multiplying, we get that: 1(or any other number)=0.
The concept of zero and that of infinity are linked, but, obviously, zero is not infinity.
If infinity exists, any finite quantity is infinitely small compared to infinity. This is a logical contradiction. That's it.
The concept of infinity varies accordingly. Mathematically, if we see infinity is the unimaginable end of the number line. As no number is imagined beyond it(no real number is larger than infinity). The symbol (∞) sets the limit or unboundedness in calculus.
Since infinity is just a concept and is not a fixed number, hence the operations like addition, subtraction, multiplication, or division do not give similar results as obtained by other numbers when operated by these operations. Infinity over infinity is Undefined.
The thing is, infinity is not a number, but a concept or idea. A "googol" is the number 1 followed by 100 zeroes. The biggest number with a name is a "googolplex," which is the number 1 followed by a googol zeroes.
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.
Answer and Explanation:
Any number divided by infinity is equal to 0.
Answer: Evaluate the value of 5 divided by infinity. Hence, 5 divided by infinity is 0. Alternatively, we know that any number divided by 5 is equal to 0.
Multiplication Property
If a number is multiplied by infinity, then the value of the product is also equal to infinity.
If a0 were a number c, then it would follow that a = 0 × c = 0. However, the single number c would then have to be determined by the equation 0 = 0 × c, which is satisfied by every number. We cannot assign a numerical value to 00 and instead say that division by zero is not allowed.
The rule is that anything multiplied by 0 is equal to 0. Remember this rule, and all multiplication by 0 problems will become instantly easier. If you see 0 in your multiplication problem, then your answer is 0. It doesn't matter where your 0 is located.
Yes, easily. So zero divides zero.
Factorial of a number in mathematics is the product of all the positive numbers less than or equal to a number. But there are no positive values less than zero so the data set cannot be arranged which counts as the possible combination of how data can be arranged (it cannot). Thus, 0! = 1.
Answer: 0 to the power of 2 is 0.
Let's understand the solution. Explanation: We have to calculate the square of zero, that is, 02. Now we know that zero to the power of any non-zero number is always zero.