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NO there are not..
Mathematical induction is a definite process used to prove certain mathematical equations( mostly related to series and sequences)

But mathematical reasoning is about understanding, analyzing and contradicting mathematical statement.
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They are not the same thing.

   Induction is the process of   proving a formula or theorem on the basis that , the theorem is true for one value of a variable, then proving that it is valid for the next value of the variable.  Finally, it is proven that the theorem is valid for all values of the variable.

     Usually there is only one variable (integer) on basis of which the proof by induction is based.


Reasoning is to prove a theorem, or law or principle, or to prove an equality by deriving step by step from the input to the final step.  At each step, (arithmetic and logical) formulas, theorems  and inequalities known are used to arrive at the target.

     The reasoning is usually done for all values or a subset of values of a variable or multiple variables.  There are one or more variable in most of reasoning exercises.

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