Infinity (∞) does not obey the laws of elementary algebra.
1. ∞ + ∞ = ∞
2. ∞ x ∞ = ∞
3. (a/∞) = 0, if a is finite
4. (a/0) is not defined if a ≠ 0.
5. ab = 0 iff either a = 0 or b = 0 and both‘a’ and ‘b’ are finite.
In case of limits, it is important to note that the function cannot be manipulated and cancelled as in usual algebra.
For example: (x^{2}a^{2})/(xa) = (x+a)(xa)/((xa)) = (x+a)
This can be done in general, but in limits this is not possible until and unless (xa) ≠ 0 or x ≠ a.
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