We're using the same technique used in a previous post to show that linear functions are injective. Again, all this is overkill, but I love exploring these avenues.
We are using this statement saying that if the output of a function on two numbers is equivalent, then the two numbers must be different. With some rearrangements (see this previous post) Read more ...
Showing that linear functions are injective is trivial, but using a proof by contradiction bringing up geometry is fascinating. After all, what really matters is the journey, not the destination!
We first bring up the definition of injective function Read more ...
A recent news about the distribution of prime numbers brings back the memory of a videogame that I started developing a while ago.
The game was inspired by an interesting pattern I've observed in prime numbers. There are few "islands" of prime numbers with a striking symmetric distribution. Read more ...
Few sequences of gap numbers show a symmetrical distribution.
Within the first 12 millions primes, the largest islands have a span of 11 gap numbers. The following is an example of such islands of gap numbers: Read more ...
Further exploration of shapes that can cover the plane.