China is widely suspected of supplying Russia with equipment and materials to support their war, however no-one has adduced anything concrete to support that theory so far.

The article itself doesn’t cite much in the way of sources or evidence, other than mentioning a report by Molfar, the open source intelligence agency. Molfar has published reports on the same topic in the past, but there hasn’t been anything recently.

If the Telegraph had new information or evidence they would be shouting a lot louder than this. This is most likely them covering up for a quiet day by dredging up some old rumours and repackaging them as news.

Translating a book to film is somewhat analogous to translating literature, particularly poetry, from one language to another. If the translation is too literal it risks failing in the target medium, whereas if it’s too idiomatic then it risks reshaping the source material.

In the case of LOTR, as you say, the changes made for a better film, while remaining true to the source material, and so were entirely justified. The Hobbit, on the other hand, was a complete travesty, partly because they practically rewrote the story.

“Translation is that which transforms everything so that nothing changes.”

– Günter Grass

The film was a near perfect rendition of the book. The only other case I can think of like that is LOTR.

So many things about that film are spot on - the casting, the direction, the music (Pixies, Dust Brothers). Again, LOTR also hit all the right notes in that respect.

Both of these are infinite, but the set of numbers containing odd numbers is by definition smaller than the set of numbers containing all integers, because it doesn’t have the even numbers.

This is provably false - the two sets are the same size. If you take the set of all integers, and then double each number and subtract one, you get the set of odd numbers. Since you haven’t removed or added any elements to the initial set, the two sets have the same size.

The size of this set was named Aleph-zero by Cantor.

Euler’s identity is pretty amazing:

e^iπ + 1 = 0

To quote the Wikipedia page:

Three of the basic arithmetic operations occur exactly once each: addition, multiplication, and exponentiation. The identity also links five fundamental mathematical constants:[6]

The number 0, the additive identity.
The number 1, the multiplicative identity.
The number π (π = 3.1415…), the fundamental circle constant.
The number e (e = 2.718…), also known as Euler’s number, which occurs widely in mathematical analysis.
The number i, the imaginary unit of the complex numbers.

The fact that an equation like that exists at the heart of maths - feels almost like it was left there deliberately.