Monotone and antitone functions

(not over ℝ just the domain you see = 0<x<1⊂ℝ)

These are examples of invertible functions.

∄ inverse

• I cheated on you. ∄ way to restore the original pure trust of our early relationship.
• The broken glass. Even with glue we couldn’t put it back to be the same original glass.
• I got old. ∄ potion to restore my lost youth.
• Adam & Eve ate from the tree of the knowledge of good & evil. They could not unlearn what they learned.
• “Be … careful what you put in that head because you will never, ever get it out.” ― Thomas Cardinal Wolsey
• We polluted the lake with our sewage runoff. The algal blooms choked off the fish. ∄ way to restore it.
• Phase change. And the phase boundary can only be traversed one direction (or the backwards direction costs vastly more energy). The marble rolls off the table, the leg poisoned by gangrene. The father dies at war. The unkind words can’t be unsaid.

#semigroups