Liquid Air and Compressed Air Density

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Anand Sivaram
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TL;DR
Liquid Air and Compressed Air Density
Densities of Normal Air is 1.225 kg/m3 at STP, whereas the density of Liquid Air is 870 kg/m3. That means liquid air is 710x denser that normal air.
Then suppose, we compress normal air to more than 710 atmospheric pressure, then it could have a density more than that of liquid air. Is this understanding correct?
Basically, could we compress air to that high level? Can gaseous state have more density that the liquid state? What is the typical or practial maximum pressure achieved in an air compressor? Assuming all isothermal compression used.
 
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I understood the logic of Triple Point and Critical Point. If air is cooled to 132.63K at 1bar and then compress it to 37.858 bar, it would liquefy. Above this temperature there is no liquid phase.
For water it is 647K and 218bar above which it is considered as supercritical fluid.

In that case should air at STP also be considered as supercritical fluid? Also what is the typical pressure obtained from air compressors? Industrial/Scientific ones?