OBSERVATION (nibbling)

As is well-known, an empire is weakest at its boundary. (cf: W.C. Fields’ published rant against ‘nibblers’ – nibbling probably really being a case of the cat mewing and dog having its day)

joke proof that 0! = 1

(that zero factorial equals unity)
By placing the space between the 0 and the ! on the left-hand side, we get 0 != 1, but ! before a relational symbol means the negation of the relation, and it is certainly true that 0 is not equal to 1. QED
keywords:
[Mathematics]
[Number Theory]

OBSERVATION (battle)

The silver lining of battle is its lack of sordidness.
(cf: an anti-corruption operation conducted from a dingy warehouse (as in one of the episodes of ‘The Untouchables’) – one easily forgets the sordidness of the environment)

attribution-flipping

(attribution-reversal)
example 1: ‘the thin man’ (originally referred to the murder victim, but later to the detective who solved the case)
example 2: “Any man that hates dogs and babies can’t be all bad.” (said OF W.C. Fields, but later attributed TO him.)
keywords:
[flip-flop]
[reversal]
[opposite]
[attribute-flipping]
[attribute-reversal]

an explanation, by Austin Lowder, of why zero factorial equals unity

(that is, why 0! = 1)
His explanation is given in a comment by him for the article by Merriam-Webster on ‘factorial’.
Here is his explanation:
Note that 5! = 6!/6, because 6!/6 = 1 x 2 x 3 x 4 x 5 x 6 / 6 = 1 x 2 x 3 x 4 x 5 = 5!
Continuing with this process:
4! = 5!/5 = 24
3! = 4!/4 = 6
2! = 3!/3 = 2
1! = 2!/2 = 1
0! = 1!/1 = 1
That’s his explanation.
Here is the link to the article in Merriam-Webster where his comment appears.
For factorials, the fact that 0! = 1 is merely a definition, a definition made for convenience (such as making reference to binomial coefficients). What Austin Lowder provides, therefore, cannot be a PROOF, but it IS a brilliant EXPLANATION, that is a brilliant HEURISTIC, that shows why we would want to define it so. However, by ‘going to the next level’, namely, by considering the gamma function (shifted by one unit to the left), for which factorials can be defined in a way consistent with the elementary manner, it is then a THEOREM that 0! = 1.
Here is the link to the Wikipedia article on the gamma function.

Permanent intermittent fasting

Krista Varady explains the idea and its benefits in her book ‘The Every-Other-Day Diet’.
Here is the link to the purchase option on Amazon.

Note that this is not about what to eat, but when to eat. One could say that it is therefore not really a diet, but a pattern of eating. However, the Merriam-Webster online dictionary includes the meaning of ‘regimen’ in its article on ‘diet’, which amounts to ‘pattern’. Ordinary language often conflates things, and this is just another example of that.

“A full belly makes a dull brain.”
— Benjamin Franklin

“Dine with little, sup with less,
Do better still – sleep supperless.”
— Benjamin Franklin

“In general, mankind, since the improvement
of cookery, eats twice as much as nature requires.”
— Benjamin Franklin

keywords:
[Health and Nutrition]
[health advice]
[book reference]
[book recommendation]