# Category Archives: M1F

## Division by zero in type theory: a FAQ

How can a theorem prover use the convention that 1/0=0 and still be consistent? Continue reading

## The inverse of a bijection.

Constructing the inverse of a bijection in Lean can be tricky for beginners. Continue reading

## M1F, Imperial undergraduates, and Lean

Abhimanyu Pallavi Sudhir, a current first year, has formalised the solutions to last year’s M1F final exam! Continue reading

## Blue-eyed islanders (guest post)

Thanks very much indeed to Chris Hughes, who has written up some thoughts on the blue-eyed islanders problem. Before we start, here’s the history. I (KMB) heard about this problem a few years ago, and thought it was cute, but … Continue reading

## Maths undergraduate example sheets

I’m teaching a course called M1F this term — the basic “introduction to proof” course which all first year maths (and joint maths/computing) students have to take at Imperial College London. The course is supposed to be managed via our … Continue reading

## Happy birthday Xena!

It was a year ago today that I emailed Inkeri Hibbins, a wonderful administrator at Imperial College London, and asked her if she could email all the Imperial maths and joint maths/computing undergraduates and tell them about my new Thursday … Continue reading

## Complex numbers! And M1F theorems.

Lean now has complex numbers! Now all we need is sine and cosine and we might be able to prove de Moivre’s theorem! The reason I’m interested in this is that I thought that it would be interesting project to … Continue reading

## Rational powers

Lean’s core library has no support for rational or real numbers š¦ They are however in the maths library — or we can just make some fake real numbers and use them instead. — let’s define the real numbers to … Continue reading

## Sheet 1 Q2,Q3

I’ve solved Q2 and Q3 of M1F Sheet 1 and pushed the solutions to github. Q4 I somehow want to persuade Xena to do herself, but I don’t quite know the best way to do this. These questions were much … Continue reading

## First question done!

I have finally typed up full proofs for Xena, for the first question of M1F sheet 1. Here are the questions in traditional PDF format: Example Sheet 1. Here’s a link to a live Lean session containing theĀ Solutions to all … Continue reading