Proof that the past, present, and future are indistinguishable

# Proof<br><br>Consider a point in time $x$ with future $F(x)$ and past $P(x)$.<br><br>\begin{align*}<br>x&=P(x)\cup F(x)\\<br>\end{align*}<br><br>If past $P(x)\neq$ future $F(x)$, then $F(x)\cap P(x)\neq\emptyset$<br><br>But then it follows that $x\cap F(x)\cap P(x)\neq\emptyset$.<br><br>In other words, there are points in time $t$ such that $t\in\{x\cap F(x)\cap P(x)\}$.<br><br>But then<br><br>\begin{align*}<br>t\cap F(x)&\neq\emptyset\\<br>t\cap P(x)&\neq\emptyset\\<br>t\cap x&\neq\emptyset.<br>\end{align*}<br><br>But then $t\cap x=\emptyset$, which is a contradiction.<br><br>Therefore, $P(x)$ must be indistinguishable from $F(x)$. In other words,<br><br>\begin{align*}<br>x&=P(x)\cup F(x)\\<br>x&=P(x)\cup P(x)\\<br>x&=P(x)<br>\end{align*}<br><br>In other words, the past is indistinguishable from the future.<br><br>&#x200B;