#Nerdle is like #Wordle but with digits and simple #arithmetic.

#puzzles #notWordle

nerdlegame 713 3/6

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https://nerdlegame.com/

Have you ever wondered why an integer is evenly divisible by 3 if and only if the sum of its digits is divisible by 3?

Of course you have.

Well here's why

Incidentally, this rule is of course recursively applicable.

Take the number 160,851,325,561,311. It's digits sum to 48.

Suppose you don't know from memory that 48 is divisible by 3.

The sum of 4 and 8 is 12, which you probably know is divisible by 3.

But even if you don't, 1 + 2 is 3, which is clearly divisible by three.

#Arithmetic #NumberTheory #Fun

https://www.cuemath.com/questions/prove-that-if-the-sum-of-the-digits-is-divisible-by-3-the-number-is-divisible-by-3/

Reminded by an article posted about by @Rhysy, I came to think of the difference between difference and similarity (or vice versa) - I think I've already written about how this difference (or indeed similarity) is like a reversible sweater. The two concepts are intrinsically two sides of the same coin, and anything that can be described as similar to something else can also be described as different from that same thing.

But I am not sure I have really written about abstractness, which might be an oversight, considering how much opinions I have on the matter.

My taxonomy if abstraction is really very simple (if black-boxy), and also quite predictable, if you know me at all:
Abstraction is the act (or its product, because english is like that), of inductively deriving a pattern from a bunch of observations, or a bunch of ideas, and maybe of bunches of things too abstract to name. In simple terms, there are measuring points from which we abstract their relation, like an extrapolation.

In this taxonomy, arithmetic is an abstraction from counting, which again is abstracted from the idea that things are not unique (vis a vis my oft-mentioned threeness piece https://medium.com/@ansugeisler/threeness-25185def6ab7 ).
Math, or at least its starting seed, is in turn an abstraction from arithmetic, and what a can of worm that is...

The post that stirred up this train of thought was about whether wasps can be said to have an abstract concept of "sameness" just because they can be shown/trained to react to instances of "same".

The connection to Set Theory seems unavoidable. "Sameness" does not belong to the set of "Same", nor does "Same" belong to the set of "Sameness". In my taxonomy of abstraction, I put it this way: A relation between individual measuring points doesn't include the measuring poinnts. Similarly, although the measuring points embody the relation, the relation is not a part of the measuring points.

#philsophy #math #science #arithmetic #AtMePls