Can you go from pure mathematics to real world mathematical applications?
The answer is, no. You can not start with math only and then apply to real-world scenarios. It is, however, possible to use mathematics in the real world (even in the fictional world, as in the Harry Potter and movie stories), but the path and direction of the applications are different and need to be clarified.The reason you can not go from pure mathematics to real-world math applications is in the nature,the definition (in a sense) of a number.
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