… I mean… yes, the logic follows… if you… make and hold that assumption… which is ostensibly what you are trying to prove.
This is otherwise known as circular reasoning.
Apparently this arose basically as a joke, a way of illustrating that you actually have to prove the induction is valid every step of the way, instead of just asserting it.
It’s not circular reasoning, it’s a step of mathematical induction. First you show that something is true for a set of 1, then you show that if it’s true for a set of n it is also true for a set of n+1.
No, that’s what induction is. You prove the base case (e.g. n=1) and then prove that the (n+1) case follows from the (n) case. You may then conclude the result holds for all n, since we proved it holds for 1, which means it holds for 2, which means it holds for 3, and so on.
From that link:
… I mean… yes, the logic follows… if you… make and hold that assumption… which is ostensibly what you are trying to prove.
This is otherwise known as circular reasoning.
Apparently this arose basically as a joke, a way of illustrating that you actually have to prove the induction is valid every step of the way, instead of just asserting it.
It’s not circular reasoning, it’s a step of mathematical induction. First you show that something is true for a set of 1, then you show that if it’s true for a set of n it is also true for a set of n+1.
No, that’s what induction is. You prove the base case (e.g. n=1) and then prove that the (n+1) case follows from the (n) case. You may then conclude the result holds for all n, since we proved it holds for 1, which means it holds for 2, which means it holds for 3, and so on.