paradox of opposite day


Jun 16, 2012
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Since opposite day starts by you saying that it's opposite day, basically it's not opposite day because you said it was opposite day and since it's opposite day, you said that it's not opposite day, so if you said it was opposite day while it just became opposite day, you're really saying that it's not opposite day. If you said that it's not opposite day without it being opposite day until you say that it's opposite day, it still can't become opposite day because it's not opposite day, and since it isn't opposite day it wouldn't be opposite day until you say it's opposite day and then it wouldn't be opposite day and it would keep going like that.

Bind blown yet?


Aug 6, 2011
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This is quite easy to solve using discrete math. Let 'x' equal the phrase "opposite day" spoken by person 'A'. Now, let 'y' equal all inverse logic that happens on opposite day.

We can set up the equation. A * x = y. (Meaning, a person saying it's opposite day, on opposite day, thus the inverse logic of 'y' for the phrase comes into play.)

Now, what we want to do, is to PROVE whether it truly is opposite day or not, using this equation. To do that, we need to get 'x' by itself.

x = y/A

Now this proves that the phrase "opposite day" is TRUE if person A is using inverse of his/her words. (basically lying)

This still doesn't answer our question to prove if it's truly opposite day or not though. So let's take it further. Now let's see what happens if we can make our lying person, tell the truth. To do that, we need to get 'A' by itself, and be sure it's not 1/A. Like so;

y/x = 1/A <-- not quite right so we take the reciprocal.
x/y = A <--- that's better.

So now person 'A' is telling the truth when he uses phrase "opposite day" inversely (which, it can only be used inversely on opposite day.)

And when someone uses the inverse of "opposite day" they are saying its NOT opposite day. Therefore, we can conclude opposite day (the day for inversed logic) does not exist.

And this children, is how you use math. DISCRETE MATH. Properly. Thank you. :)