Choice of public key and private key in RSA

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I am trying to dig as deep as I can into the RSA algorithm and trying to wrap my head around why the public key and it’s mod inverse have to be less than $\varphi(n)$. $\varphi(n)$ is the number of numbers that are co prime with $n$ right ? And not the actual number that is coprime. How is picking numbers less than $\varphi(n)$ helping ?