Final answer:
Adding any finite number to infinity gives a result of infinity, as infinity is an unbounded quantity. Infinity can't be treated like a regular number and does not follow the normal rules of arithmetic such as the commutative property of addition.
Step-by-step explanation:
When we talk about infinity, we are dealing with a concept rather than a specific number that can be manipulated like integers or real numbers. In the realm of mathematics, infinity symbolizes an unbounded quantity that is larger than any real number. Because of this, traditional arithmetic operations like addition and subtraction work differently when infinity is involved.
Adding any finite number to infinity does not change the nature of infinity. It remains an unbounded quantity. So, for example, when we add 3 to infinity, mathematically expressed as 3 + ∞ (infinity), the result is still infinity. This can be confusing because with ordinary numbers, adding two values together changes the sum, as expressed in the commutative property of addition, A + B = B + A. However, when dealing with infinite values, this property no longer applies in the same way.
It is important to note that infinity is not a number that follows arithmetic rules, such as when two positive numbers add, the answer has a +ve sign, or in multiplication and division. Instead, infinity represents a sort of limit, a concept where quantities can grow without bounds.