City Tutoring Discussion Forum

If our fundamental properties are true purely because we made some definitions and assume those definitions are true, then there is nothing to distinguish them from an arbitrary dogma.

The way I view the entirety of math is the same way I view individual sections of abstract algebra. Those ...

You have no clue as to the reason for WHY these fundamental properties you listed are valid


Yes I do? All the properties I listed are either basically definitionally true (like substitution) or derivable from their definitions (commutativity, distributivity etc.). I don't view mathematics as ...

However, I would argue with the notion that it is immoral to restrict the spread of information. The ability to spread information quickly is not a thing that can be used neutrally. Every person who acts upon that ability to spread their ideas is not spreading a neutral substance to the population ...

I dont think I agree with the premise that using algebra or computational reduction to solve for variables is fundamentally different or even uninteresting compared to some abstract notion of the "essence of an expression", and as a matter of fact I think algebra takes the notion of the "essence of ...

Whoa cool stuff. Noob here, So what exactly is this computational way of proving things?


There are two major components to the proof assistants, the proof checking and the automation. The proof checking is simply that the computer can tell whether a proof actually proves a statement or if it ...

I never formally studied Category Theory but it was all the rage in my Logic class and felt like the inevitable next step - would you say with a decade out of full time instruction there's a best way to pick it up again or build up to it?


Honestly, all the books I've come across are extremely ...

I've messed around with Rocq about a year ago, half a year ago I picked up "Type Theory and Formal Proof" by Hermann Geuvers and Rob Nederpelt (highly recommended for understanding the base CoC) and more recently I have been learning Lean 4. The primary project Ive been working on is learning ...

You've made me rethink my view on the rapid spread of information, I do now think the printing press has fundamentally changed the interaction of individuals with the society. We also agree that much of the problem is individuals being the final judges of right and wrong, as it ignores the countless ...

There's no doubt mathematics in public education is filled with half baked explanations, subpar instruction and most worriedly the rejection of any question of why something is the way it is beyond whats necessary to traverse the path between the question and the answer. This has given rise to a ...

Modern news has made it clear that the printing press and in general everybody having access to any information isn't a simple positive, though that's true for any mechanism for spreading ideas. I would say that it has increased the "standard deviation", so to speak, of general wisdom in the ...