It was found that freezing of water in terms of homogeneous nucleation of ice never occurs even in ultra-clean micro-sized water droplets under normal conditions. More surprisingly, at sufficiently low supercoolings, foreign nano-particles exert no effect on the nucleation barrier of ice; it is as if they physically "vanished." This effect, called hereafter the "zero-sized" effect of foreign particles (or nucleators), leads to the entry of a so-called inverse homogeneous-like nucleation domain, in which nucleation is effectively suppressed. The freezing temperature of water corresponds to the transition temperature from the inverse homogeneous-like nucleation regime to foreign particle-mediated heterogeneous nucleation. The freezing temperature of water is mainly determined by (i) the surface roughness of nucleators at large supercoolings, (ii) the interaction and structural match between nucleating ice and the substrate, and (iii) the size of the effective surface of nucleators at low supercoolings. Our experiments showed that the temperature of -40 degrees C, commonly regarded as the temperature of homogeneous nucleation-mediated freezing, is actually the transition temperature from the inverse homogeneous-like nucleation regime to foreign particle-mediated heterogeneous nucleation in ultra-clean water. Taking advantage of inverse homogeneous-like nucleation, the interfacial tensions between water and ice in very pure water and antifreeze aqueous solutions were measured at a very high precision for the first time. The principles of freezing promotion and antifreeze and the selection for the biological ice nucleation and antifreeze proteins are obtained. The results provide completely new insights into freezing and antifreeze phenomena and bear generic implications for all crystallization systems.