What is Half of Infinity in Math?

Half of infinity is still considered to be infinity.

Here's a more detailed explanation:

Infinity isn't a real number; it's a concept representing something without any bound or limit. Therefore, you can't apply standard arithmetic operations like division to it in the same way you would with numbers.

• Infinity as a Limit: In calculus, infinity often arises when we consider limits. For example, the limit of x as x approaches infinity is infinity. If we consider the limit of x/2 as x approaches infinity, the result is still infinity. The function x/2 continues to grow without bound as x increases without bound.

• Indeterminate Forms: Expressions like infinity/infinity are called "indeterminate forms." This means that the value of the expression cannot be determined solely from the fact that both numerator and denominator are infinitely large. You need more information (e.g., the functions involved) to determine the actual limit (if it exists). Infinity divided by infinity is not always equal to 1.

• Cardinality: In set theory, infinity can describe the size (cardinality) of a set. For example, the set of natural numbers {1, 2, 3, ...} is infinitely large. Dividing an infinite set conceptually in half, would simply create two infinite sets. Each half still possess an infinite number of members.

Essentially, trying to treat infinity like a regular number and performing arithmetic operations can lead to inconsistencies.