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There's a simple mechanical transformation from one path to the other. As a proof that "the store is reachable, they are essentially the same if it is already
by lupire 2y ago
There's a simple mechanical transformation from one path to the other.
As a proof that "the store is reachable, they are essentially the same if it is already known that you live on a "block" with the store" . If it is not known that you live on a block, then the second proof together with the first gives a much deeper result, proving that you do live on a block. That makes a second proof valuable, but in the monograph of history, it is most parsimonious to make the block proof and the note how it implies to trivially distinct ways of reaching the store.
- ColinWright 2y agoSo you are saying that the two proofs are different, but there is a third proof that gives each of the first two as corollaries. So ... the first two proofs are different, then.
- lupire 2y agoThat's one opinion. The OP and I have a different opinion.
- Y_Y 2y agoNeglect considerations of homotopy at your peril!
- gus_massa 2y agoYep. If you can go from A to C by B or B' and all the place is a nice grass field they are probably equivalent. But if between B anb B' there is an active vocano, most people would call the paths different.