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"1/0" is a paradox; in a way that "0/1" is not. Nothing can be divided by zero. If one approaches the formula from the positive side, it would appear that the answer is an infinite positive value. If one approaches the formula from the negative side, the opposite is true. Thus, anything divided by zero is simultaneously positive and negative infinity. "One over Zero" is a paradox in another way too, in a way that transcends mere arithmetic. One is something, and Zero is nothing. The fact that the universe holds something over nothing, that it prefers to exist, rather than not exist, is fundamentally absurd. No being can ever come to deserve its own birth. 1/0 is a cry out against mere logic and efficiency. Stuff exists. All existence, all truth, cannot be ultimately justified: it can only be described, explained, and enjoyed.
1/0 is illogical. 1/0 is irrational. 1/0 is impossible. 1/0 is transcendentally unfair.
1/0 is true. Deal with it.