Jane writes
I've got a lovely, large old cactus that got a little bit damaged when
I recently moved house. One of its many 'arms' (wonder what they are
called? It really does look like it's spreading its arms out to take a
bow) got damaged near the 'trunk' of the plant and I had to cut it off.
I trimmed it down a bit and put it in a little bit of water and I was
wondering if it would continue to grow, if I should put it in cactus
compost or something. Any ideas?

Take it out of the water!

Leave it around for a few weeks to let the cut end callous over. Then
prop it up on some free draining compost and you have a fair chance of
it rooting. That is, if it is a cactus and not one of the succulent
plants that sometimes are loosely referred to as cacti.
--
Kay