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First day of Discrete Math đź’€
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this post was submitted on 29 Apr 2025
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I mean I'm definitely noticing the patterns. I'm just frustrated that someone who is supposedly an expert in logic let something like that slip. Not assuming that logical negation means "opposite" is one of the first things they teach you. For example, if we were thinking in opposites, the negation of "all" would be "none." But the negation of "all" is "not all", where the negation of "none" is "at least one."
That’s not how it’s usually going to work in discrete - that’s the message the book is trying to communicate to you.
Think like an engineer designing a computer. The state of the weather is something that we are introducing as a binary here - bad or not bad, good or not good.
I’m sure the next few chapters will talk about things like truth tables, right? Try to imagine what those would look like with a “trinary” logic system. Remember math is a tool we use to abstract reality efficiently.
@andros_rex @SuperNovaStar Picking something as continuous as "the weather" to explain negation is just stupid.
Pick something like "locked" or "unlocked".
Yes, there's a transition, and we all wave our hands and pretend it isn't there. The same thing happens in Boolean algebra, when negating something.
Best not to get involved with "all", "none", "null". Because you've left out "some", "many", "any", "few", "more", "less", and a host of more subtle values.
@andros_rex @SuperNovaStar Programming languages do logic a lot of injustice, often assuming certain values are false, most values are true, and a few are weird (like "none"). Those are implementations for practical reasons, and not pure math.
Exactly. And sometimes you need to understand the underlying logic well before you even try to program anything. It is far easier to know set theory and then adapt that knowledge to programming than to learn a warped, trimmed down version of set theory just to fit programming languages and then try to derive the real thing once you run into a problem that needs it.