In fact the unaided-eye or naked-eye visible stars can be numbered approximately. The approximation is due to the fact that how many you can see depends on latitude, elevation, horizon shape, altitude of the star, weather, and your particular vision acuity. The normal human eye can see down to a visual magnitude of about 5.5. There are about 2800 stars of at least this brightness. Now only about half the celestial sphere is visible at once and so that sets an upper limit of about 1400 stars. Then there is atmospheric extinction. Stars at low altitudes are seen through more air mass, and so are fainter than at higher altitude. Thus some of the 1400 stars will be fainter than 5.5 magnitudes. (I assume my source means that those 2800 stars of greater than or equal to 5.5 magnitude have their magnitudes measured at zenith under clear skys.) At Australia's latitude more stars are visible than elsewhere and all that can normally be seen on a clear night is about 950.
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Note web pages tend to disappear, but sometimes they are the best one can do.