Highest magnifications

Using a bit of mathematics i have been looking into degrees,
arcseconds and so on.

Having verified the moon to be .5 degrees, and the sun to be about the
same - and this agreeing with books - i was happy that i was doing the
right thing.

When getting say x2 magnification does that mean we see the moon as if
it was 1 whole degree? it ought to follow.

I used the same calculations on nearby stars to fully appreciate why
we just can't see them as disks through telescopes, i roughly
estimated that seeing Sirius A as a disc roughly the size of the moon
would require x300,000 magnification (but i may have that wrong):

360 / 2Pi =57.3 (used later)

Moon degrees = 57.3 * arctan(diameter/distance) (thats roughly
3476/384000)
= just over 0.5 degrees

Sirius A degrees = 57.3 * arctan(1390000km/8.6ly)
(ly=9,460,530,000,000km)
= 0.000001645 degrees
multiply that by 300,000 to get just under .5 degrees!

but please do correct any errors, it's a first bash at this.

What is the highest magnification realistically available to amateurs
and the best amatuer scope in realistic seeing. A really huge mirror
in space, or an even bigger one built on the moon, would perhaps get
to the point of being able to see nearby stars as discs.

I'm still impressed by the idea of seeing something at x80 !

I understand that the HST saw a red giant (betelguese?) as a tiny
disk.

btw, i hadn't appreciated how big in the sky andromedia is - i guess
it's because we generally only see the smaller central part.