Number of stars in sky

How many stars can be seen by telescope?

Eye has standard angular resolution of about 1 minute (or larger) and
can see magnitude 6.

There are estimated to be something of 5000 to 6000 stars up to
magnitude 6 - over the whole heavenly sphere.

The whole sphere should be something like 40 000 square degrees, or
150 millions of square minutes. So, out of the 150 million pixels of
whole sky, 6000 are point sources of light, and the rest, 25 000 times
more, is empty dark sky.

What is the now resolution of telescopes? 0,1 seconds? 0,01 seconds?

And what is the magnitude telescopes can see? +21? +25? +30?

How many stars (point sources of light which can be seen by telescope,
resolved from others and believed to be a star or a close multiple)
can be observed in sky?