I have a math intuition I've struggled with my whole life and would be very indebted if someone could help me think clearly about this. I currently think about it as "intervals" vs "indices". (thread)
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Some examples: to me it feels numerically unintuitive that if a Friday is the 3rd, Monday is the 6th. Weekends are two days long. My brain always wants to jump to the math 3 + 2 = 5, so I expect Monday to be the 5th.
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Another example: it's unintuitive to me that the set of pool balls 6-10 is a set of 5 balls. Same reason. I want to jump to 10 - 6 = 4, so it *feels* like it should be 4 balls.
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The missing intuition seems to be when numbers are describes indices, or when they're describing intervals. From Friday to Monday, there are 2 indices (Sat, Sun), but three intervals (Fri - Sat, Sat - Sun, Sun - Mon).
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The weekend problem is made worse by other weekday math that *feels* similar. If today is Tuesday the 9th, and I want to know what day next Tuesday is, I can safely add the number of days in a week to find out. 9 + 7 = 16. So next Tuesday, a week from the 9th, is the 16th.
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I can't seem to intuit when I'm doing intervals vs. indices and how that affects the subconscious math. Another way I sometimes think about it is figuring out whether I'm operating on inclusive/exclusive ranges, but I struggle even more to verbalize that explanation.
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(I realize this sounds like the legendary and much-lol'd body building forum thread about working out every day lmao but it's a genuine problem)http://gawker.com/bodybuilders-try-fail-to-calculate-number-of-days-in-1677545788 …
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This missing intuition has slowed me down my entire life because I always feel compelled do double and triple check whether I'm operating on indices or intervals. Does anyone have a clearer way to think about this?
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Replying to @benedictfritz
Haha, same here. This is basically a summary of what you already said but.. it's a pretty common problem to have apparently: https://betterexplained.com/articles/learning-how-to-count-avoiding-the-fencepost-problem/ …
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Oh man this looks like exactly it! Excited to dig in and see if I can find something new :D
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