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The stacking paradox

שו”תCategory: Talmudic studyThe stacking paradox
asked 7 years ago

[99.99% that you know this, but the epsilon chance that it will interest you is giving me no rest]

Toss 19: D. Makosh.


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מיכי Staff answered 7 years ago
I didn’t know that, and that’s definitely interesting. At first I thought it wasn’t a matter of the stacking paradox but of infinity. After all, the last epsilon is as small as you want, and therefore there is an epsilon here that is equal to 0, and in the limit where it goes to 0, it is no less than a hundredth of a penny, but an actual zero (if you assume that there is a hundredth of a penny here, you can always cross it out and say that it is not that, but only half of that, and so on). This raises the question of whether an epsilon that is as small as we want is the same as an actual zero or not (an epsilon is a small segment, so its dimension is 1 and its length is 0. A point has dimension 0 and has no length). Although in pickaxe blows it is of course not continuous and each blow has some final value. The question is whether these are really pickaxe blows or whether it is just a form of expression to say the value of the end of the work, and then I am still right. It must also be rejected that a non-Gentile less than the Epsilon also has value, but the question is how much less. And in something Epsilon there is no value even for a non-Gentile. Here the question of the heap of course arises (since when is there no value). This reminds me of the words of Rabbi Abba Shaul, who was asked whether it is permissible to drink water from the Sea of ​​Galilee on Passover because of concerns that someone threw a piece of bread (leaven in something), and he answered that even something has a measure. And Dfah. Incidentally, here the solution is clearly as I said. The value is according to the size of the Epsilon (and not dichotomous: there is or there is no value). And Zela, is the value in the eyes of man dichotomous: either he gives it value or not (what is important enough in his eyes). Or is this also a heap and the threshold for cutting is only legalistic-halachic.

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