What does Infinity Minus Infinity Equal?
At first, you may think that infinity subtracted from infinity is equal to zero. After all, any number subtracted by itself is equal to zero, however infinity is not a real (rational) number. I am going to prove what infinity minus infinity really equals, and I think you will be surprised by the answer.
First, I am going to define this axiom (assumption) that infinity subtracted from infinity is equal to zero:
| ∞ - ∞ = 0 |
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Next, I am going to add the number one to both sides of the equation.
| ∞ - ∞ + 1 = 0 + 1 |
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Since ∞ + 1 = ∞ and 0 + 1 = 1, then we are going to simplify both parts of the equation:
| ∞ - ∞ = 1 |
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Woops! It is impossible for infinity subtracted from infinity to be equal to one and zero. Using this type of math, we can get infinity minus infinity to equal any real number. Therefore, infinity subtracted from infinity is undefined.
by Phil B.