As per my knowledge, degrees of freedom of any physical system are the number of independent quantities(coordinates) which need to be specified in order to specify the state of a system uniquely. However, my question is, why is there a unique number of degrees of freedom for any system?
Or, to put it differently, if a set of $n$ independent coordinates describes the state of the system completely, why is it true that any other set of $n$ independent coordinates also describes the state of the system completely?
And why can there not be a set of $m$ independent coordinated which also describe the state of the system completely, where $m>n$ ?
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