Sy123
This too shall pass
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- 2013
So I was thinking of whether the following inductive statements are logically valid:
Say we have 2 statements,
and ![](https://latex.codecogs.com/png.latex?\bg_white S_2 )
![](https://latex.codecogs.com/png.latex?\bg_white \\ $For the base case,$ \ S_1 \ $is true, assuming$ \ S_1 \ $is true for the general case, then if$ \ S_2 \ $is true, then the inductive step for$ \ S_1 \ $is true$ )
![](https://latex.codecogs.com/png.latex?\bg_white \\ $For the base case,$ \ S_2 \ $is true, assuming$ \ S_2 \ $is true for the general case, then if$ \ S_1 \ $is true, the inductive step for$ \ S_2 \ $is true$ )
![](https://latex.codecogs.com/png.latex?\bg_white \\ $Therefore$ \ S_1 \ $and$ \ S_2 \ $are both true for all cases$ )
So as you can see, both inductive steps are connected to each other in a sort of circle, does it still count as circularity considering we are only assuming it for an inductive step?
Say we have 2 statements,
So as you can see, both inductive steps are connected to each other in a sort of circle, does it still count as circularity considering we are only assuming it for an inductive step?
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