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WM laid this down on his screen :
If there was a bijection, then the whole axis could become red.Let every unit interval after a natural number on the real axis be coloured white with exception of the intervals after the prime numbers which are coloured red. It is impossible to shift the red intervals so that the whole real axis becomes red. Every interval (10n, 10 (n+1)] is deficient - on the whole real axis.So what? Your imaginings don't affect the fact that there is a bijection.
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