Is infinity a number?

Question: Is infinity a number?

Answer: No.

However, it's tempting often to treat the (positive or negative) infinity a special kind of number because it behaves like one sometimes:

• you can add and multiply infinities (but not subtract or divide);
• you can perform all four algebraic operations with infinity and a finite number;
• you can compare infinity and any finite number;
• you can add a point to the real line and treat this point as the "location" of infinity.

Infinity should be treated properly via limits.