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Cake day: July 11th, 2023

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  • My favorite version of this proof:

    Let S be the subset of natural numbers that are not interesting. Suppose by way of contradiction that S is inhabited. Then by the well ordering principle of natural numbers, there is a least such element, s in S. In virtue of being the least non interesting number, s is in fact interesting. Hence s is not in S. Since s is in S and not in S, we have derived a contradiction. Therefore our assumption that S is inhabited must be false. Thus S is empty and there are no non interesting numbers.


  • A group is not an algebra. A group consists of a single associative binary operation with an identity element and inverses for each element.

    A ring is an abelian (commutative) group under addition, along with an additional associative binary operation (multiplication) that distributes over addition. The additive identity is called zero.

    A field is a ring in which every nonzero element has a multiplicative inverse.

    A vector space over a field consists of an abelian group (the vectors) together with scalar multiplication by elements of the field, satisfying distributivity and compatibility conditions.

    A non-associative algebra is a vector space equipped with a bilinear multiplication operation that distributes over vector addition and is compatible with scalar multiplication.

    An (associative) algebra is a non-associative algebra whose multiplication operation is associative.

    You can read more about these definitions online and in textbooks - these are standard definitions. If you are using different definitions, then it would help your case to provide them so we can better understand your claims.

















  • I agree that anecdotes aren’t worthless, but for different reasons. There’s actually a saying that goes, “the plural of anecdote isn’t data.” Anecdotes are just stories. They aren’t data points and they aren’t peer reviewed. If you want to turn anecdotes into data, you have to do the proper interviews and surveys to actually build a dataset and then get the peer review, but at that point we aren’t talking about anecdotes anymore.