Proving that divisibility is transitive

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in this video we practice our structure for formally proving statements. In this case, it is a proof about divisibility, namely that divisibility is transitive. We follow the proof structure of assumption, definition of assumption, manipulation, definition of conclusion, and finally conclusion.

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  1. Dr. Trefor Bazett
  2. Discrete Math
  3. Divisibility
  4. Transitive
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  6. assumption
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Комментарии
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I can't pay fees rn but I'll be your potential patreon after I get a job. For now I watch ads and click on em. 😬

surinderkaur
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It took me a while to get the last proof. When I wrote it down myself it made sense 🤣 Thanks for all your effort again 😀

christopherbarrett
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I’m literally going to cry, this was so helpful. I’ve been struggling to understand this in class and I have a test tomorrow

ayeoritseyemi
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I really love the way you speak, , , makes listening to you very easy😇

aurumstinger
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why do you use | for division? In an earlier video you use | to shorthand "such that" with {x | P(x)}. In the context of this video it is clear that | is representing division, however if I was just looking at the formula, I might deduce a|b as a "such that" b rather than a divide by b. Why not use / a/b?

uridimmuvltozwta
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Great video. Really cleared all my doubts. I was having trouble understanding Elementary Number Theory by David Burton.

piusadas
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Are you writing everything backwards? I’m calling the police.

ZoomerAdvice
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Great video! Regarding the definition of divisibility: the d =/= 0 requirement was added to set any expression that is divided by 0 as undefined, right? Since, if d were allowed to be 0, then though no integer k exists such that, for instance, 5 = 0 * k, it would now be the case that 0 does not divide 5, instead of that 5 / 0 is not defined. Similarly, if n = d = 0, then 0 would divide 0 but the result would not be a number but rather the entire set of integers since for any integer k it is the case that 0 * k = 0.

gilkeidarmusic