> Nikon wouldn’t want to use their competitor’s innovation on their flagship
Not sure where the author gets this idea, especially considering that the Z9 uses a sensor made by Sony [0]. Yes, technically it is made by Sony Semiconductor and not Sony Imaging, but they are still the same company.
Many people here are recommending texts like How to Prove It by Velleman. From this book: "Many students get their first exposure to mathematical proofs in a high school course on geometry. Unfortunately, students in high school geometry are usually taught to think of a proof as a numbered list of statements and reasons, a view of proofs that is too restrictive to be very useful."
One solution to this problem is to learn from a book purely on proofs, as Velleman suggests. It seems to me, however, that given your background and your wish for an 'exceedingly gentle introduction', this method might not be the best for you.
While I agree with the view that the attachment between geometry and proofs is detrimental to students' learning of both topics, I would like to make the argument that in a case like yours, learning proofs through geometry is actually a great place to start.
Proofs are not traditionally linked to geometry without reason; in school, geometry is the closest thing you get to "real" mathematical thinking. Since you are already familiar with geometry, revisiting it, this time through a lens focused on proofs, would be an effective way to bridge the gap between traditional school mathematics and proof-based thinking.
At this point, it comes down to finding the right geometry book. I highly recommend Introduction to Geometry by Richard Rusczyk: https://artofproblemsolving.com/store/book/intro-geometry. While it is designed for the advanced high school student seeking to learn geometry in a different way than what is taught in school, it just so happens that this makes it a great book for your purpose as well.
Having already learned geometry, you will be able to focus more exclusively on the proof aspect of the book. Take a look at some of the excerpts listed in the link above to see if the style of the book suits what you are looking for. After learning geometric proofs, you will then be able to easily extend the same ideas to proofs in other subjects.
Exactly. Suppose a piece of software remains around for another year with probability p, and for the sake of this example, that p is constant.
Then if the software has been around for one year, the expected value of p is 50%. But if the software has been around for ten years, the expected value of p jumps to 0.5^(1/10) ≈ 93.3%.
In this way, if a piece of software has been around for longer, then it has a greater chance of sticking around. In fact, the expected number of years it has left is indeed equal to the number of years it has already been around, as stated in the article.
In practice this mechanism is more complicated, as all software is influenced by a changing environment, but this same idea is still at the core.
> Then if the software has been around for one year, the expected value of p is 50%. But if the software has been around for ten years, the expected value of p jumps to 0.5^(1/10) ≈ 93.3%.
This reasoning is incorrect.
You have to take the distribution of p into account.
In a world where almost every software has p=0.5 the software which has been around for 10 years is likely to have been lucky and not to have higher p.
