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There are seven days until Christmas. Every day, I will cancel one axiom of set theory, until there are no more axioms, and set theory will be cancelled altogether

Today, we are cancelling the axiom of pairing. Who needs pairing? You have replacement. There's no reason making a set of two sets should be handled any more specially than making a set of many sets.
🚫 pairing 🚫

A new day, another axiom cancelled. Today's cancellation is the axiom of infinity. There are so many ways of making infinite sets, why did they choose x ∪ {x} as the successor? Why not ℘(x)? They're cowards, that's why. So what if ℘⁶(∅) can't be physically written down, that is no concern of the mathematician.
🚫 infinity 🚫

And on the third day we cancel the axiom of choice. You say there's a choice function for every set? Fine. Give me a choice function for ℘(ℝ). Go on, show me. That's right, you can't.
🚫 choice 🚫

We're more than halfway there. Today we're cancelling the axiom of foundation. That's right, Zermelo and Frankel's precious well-foundedness? Yeet that in the trash. There is no reason a set should not contain itself; coinductive structures are just as valid as inductive ones. It's co-discrimination!
🚫 foundation 🚫

Good evening. The solstice is in less than one hour. I'm cancelling the axiom of the empty set. ∅ = {y ∈ x | y ≠ y}. That is all.
🚫 empty set 🚫

I'm very :seepy_cosy: but I have a duty and that is to cancel another set theory axiom. This time I'm cancelling the axiom schema of replacement for being too complicated and confusing. It's hard to figure out what to instantiate the formula inside of it as, and it's not intuitive in its pure set statement, and it's only clear that it's the image of a function when you use classes. It's also a very big axiom and I think they can stand to break it up into small pieces.
🚫 replacement 🚫

We've come down to the last few axioms now. I'm so sorry, but I have to cancel the axiom of powerset. You can't make some infinite cardinalities bigger than others if there aren't any more of them, I guess (and we already cancelled infinity, so there aren't infinite ones at all). But happy Christmas Adam!
🚫 powerset 🚫

There's only one day left. Today we cancel the axiom of union. There remains no more ways to create sets out of other sets.
🚫 union 🚫

Happy Christmas everyone! Today's the day! Finally: the axiom of extensionality is cancelled, the very core of set theory. We have now cancelled the entirety of set theory. Merry holidays!

@ionchy i would simply construct a well-ordering on ℝ and pick the least element

@ionchy next step is to cancel the rest of math

@ionchy This sounds like a threat. "Unless my demands are met set theory will be no more in 7 days."

@jordyd oh, I have no demands. my only demand is that set theory be cancelled by Christmas, even if I have to do it myself

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