Is the Avogadro constant equal to 1?

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So if 1mol=6.022x10^23, and the Avogadro constant NA=6.022x10^23x1/mol, if we substitute mol in the avogadro constant we get 6.022x10^23x1/6.022x10^23 = 6.022x10^23/6.022x10^23 = 1. Where did i make a mistake?