why Induction is Admissible?

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This question has been always intrigued me.
Why proof by Induction is admissible/acceptable ?
We use this type of proof nearly every where and some times It's the easiest way of proof.

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It's admissible because it's defined as an axiom of our arithmetic. It was chosen as an axiom because it's a proof method that works - so much so that there are variants that apply even when you're not working with the natural numbers, as long as a few other properties hold.

If you have a problem with why it works, feel free to ask it and I can try to elaborate.