How to see if a numeric range overlaps with any range present within a list of numeric range

Hello All,

I want my users to be able to set various numeric ranges.
When he creates one , how can I check that it does not already exist or part of this range overlaps with the existing list?

Second question probably more technical:

If a user has already ranges such as [ 420-540] , [520-640], how can I transform this into [420-640]?

Thank you in advance

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