How does mathematical induction actually work?
After surfing on the internet for a while, I found the following analogy.
Consider rectangular tiles (dominoes) stacked on beside the other. When we force the first tile to fall, the others begin to fall.
To actually know if all the tiles have fallen, we need to know the following-
- If the first tile has fallen or not. (If not, non of them have fallen)
- If the first tile has fallen, then we can pick some random tile from the stack to check if that has fallen. If this tile has fallen, then the previous tile must have also fallen.
- From this, we can conclude that all the tiles have fallen.
But I don't understand how this idea of induction works with numbers?
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