1st grade mathematics work sheets and my mother's mathematics teaching style. Mathematics will not be so terrible, since it seems that parents are interested in preparing their little ones for mathematics before school age.
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In light of my tweet thread about the category of finite sets and commutative monoids (https://t.co/jnY0wZZbxq), I thought I might try to say what the analogue is for braided monoidal things (although much of this is still somewhat hypothetical).
It's also just kind of a cool combinatorial structure! I've been talking to @CreeepyJoe about this lately, as well as @grassmannian.
The first thing you have to know is that, in a braided monoidal category you can still have commutative monoids. Since a braided monoidal category C has a "twist" map for every object β(x):x⊗x→x⊗x, if x is a monoid you can ask for the following diagram to commute:
Remember that being symmetric monoidal just means that if you take the twist map above and do it twice, you get the identity map, but braided monoidal doesn't mean that. But it's okay! You can still define commutative monoids here.
But so anyway, we can talk about commutative monoids in braided monoidal categories.
So okay, here's a thread on the category of finite sets and a way in which it controls algebraic structure in symmetric monoidal categories. I think it's some really pretty stuff.
— Jonathan Beardsley (@JBeardsleyMath) December 6, 2020
It's also just kind of a cool combinatorial structure! I've been talking to @CreeepyJoe about this lately, as well as @grassmannian.
The first thing you have to know is that, in a braided monoidal category you can still have commutative monoids. Since a braided monoidal category C has a "twist" map for every object β(x):x⊗x→x⊗x, if x is a monoid you can ask for the following diagram to commute:
Remember that being symmetric monoidal just means that if you take the twist map above and do it twice, you get the identity map, but braided monoidal doesn't mean that. But it's okay! You can still define commutative monoids here.
But so anyway, we can talk about commutative monoids in braided monoidal categories.
OK, I may be guilty of a DoS attack attempt on mathematicians' brains here, so lest anyone waste too much precious brain time decoding this deliberately cryptic statement, let me do it for you. •1/15
First, as some asked, it is to be parenthesized as: “∀x.∀y.((∀z.((z∈x) ⇒ (((∀t.((t∈x) ⇒ ((t∈z) ⇒ (t∈y))))) ⇒ (z∈y)))) ⇒ (∀z.((z∈x) ⇒ (z∈y))))” (the convention is that ‘⇒’ is right-associative: “P⇒Q⇒R” means “P⇒(Q⇒R)”), but this doesn't clarify much. •2/15
Maybe we can make it a tad less abstruse by using guarded quantifiers (“∀u∈x.(…)” stands for “∀u.((u∈x)⇒(…))”): it is then “∀x.∀y.((∀z∈x.(((∀t∈x.((t∈z) ⇒ (t∈y)))) ⇒ (z∈y))) ⇒ (∀z∈x.(z∈y)))”. •3/15
Maybe a tad clearer again by writing “P(u)” for “u∈y” and leaving out the quantifier on y, viꝫ: “∀x.((∀z∈x.(((∀t∈x.((t∈z) ⇒ P(t)))) ⇒ P(z))) ⇒ (∀z∈x.P(z)))” [✯]. Now it appears as an induction principle: namely, … •4/15
… “in order to prove P(z) for all z∈x, we can assume, when proving P(z), that P(t) is already known for all t∈z∩x” (n.b.: “(∀z.(Q(z)⇒P(z)))⇒(∀z.P(z))” can be read “in order to prove P(z) for all z, we can assume Q(z) known when proving P(z)”). •5/15
\u2200x.\u2200y.((\u2200z.((z\u2208x) \u21d2 ((\u2200t.((t\u2208x) \u21d2 (t\u2208z) \u21d2 (t\u2208y)))) \u21d2 (z\u2208y))) \u21d2 (\u2200z.((z\u2208x) \u21d2 (z\u2208y))))
— Gro-Tsen (@gro_tsen) February 12, 2021
First, as some asked, it is to be parenthesized as: “∀x.∀y.((∀z.((z∈x) ⇒ (((∀t.((t∈x) ⇒ ((t∈z) ⇒ (t∈y))))) ⇒ (z∈y)))) ⇒ (∀z.((z∈x) ⇒ (z∈y))))” (the convention is that ‘⇒’ is right-associative: “P⇒Q⇒R” means “P⇒(Q⇒R)”), but this doesn't clarify much. •2/15
Maybe we can make it a tad less abstruse by using guarded quantifiers (“∀u∈x.(…)” stands for “∀u.((u∈x)⇒(…))”): it is then “∀x.∀y.((∀z∈x.(((∀t∈x.((t∈z) ⇒ (t∈y)))) ⇒ (z∈y))) ⇒ (∀z∈x.(z∈y)))”. •3/15
Maybe a tad clearer again by writing “P(u)” for “u∈y” and leaving out the quantifier on y, viꝫ: “∀x.((∀z∈x.(((∀t∈x.((t∈z) ⇒ P(t)))) ⇒ P(z))) ⇒ (∀z∈x.P(z)))” [✯]. Now it appears as an induction principle: namely, … •4/15
… “in order to prove P(z) for all z∈x, we can assume, when proving P(z), that P(t) is already known for all t∈z∩x” (n.b.: “(∀z.(Q(z)⇒P(z)))⇒(∀z.P(z))” can be read “in order to prove P(z) for all z, we can assume Q(z) known when proving P(z)”). •5/15
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H was always unseen in S2NL :)
Those who exited at 1500 needed money. They can always come back near 969. Those who exited at 230 also needed money. They can come back near 95.
Those who sold L @ 660 can always come back at 360. Those who sold S last week can be back @ 301
Those who exited at 1500 needed money. They can always come back near 969. Those who exited at 230 also needed money. They can come back near 95.
Those who sold L @ 660 can always come back at 360. Those who sold S last week can be back @ 301
Sir, Log yahan.. 13 days patience nhi rakh sakte aur aap 2013 ki baat kar rahe ho. Even Aap Ready made portfolio banakar bhi de do to bhi wo 1 month me hi EXIT kar denge \U0001f602
— BhavinKhengarSuratGujarat (@IntradayWithBRK) September 19, 2021
Neuland 2700 se 1500 & Sequent 330 to 230 kya huwa.. 99% retailers/investors twitter par charcha n EXIT\U0001f602
First thread of the year because I have time during MCO. As requested, a thread on the gods and spirits of Malay folk religion. Some are indigenous, some are of Indian origin, some have Islamic
Before I begin, it might be worth explaining the Malay conception of the spirit world. At its deepest level, Malay religious belief is animist. All living beings and even certain objects are said to have a soul. Natural phenomena are either controlled by or personified as spirits
Although these beings had to be respected, not all of them were powerful enough to be considered gods. Offerings would be made to the spirits that had greater influence on human life. Spells and incantations would invoke their
Two known examples of such elemental spirits that had god-like status are Raja Angin (king of the wind) and Mambang Tali Arus (spirit of river currents). There were undoubtedly many more which have been lost to time
Contact with ancient India brought the influence of Hinduism and Buddhism to SEA. What we now call Hinduism similarly developed in India out of native animism and the more formal Vedic tradition. This can be seen in the multitude of sacred animals and location-specific Hindu gods
i wonder if you can make a thread bout witchcraft in malaysia.. or list of our own local gods/deites..
— r a y a \U0001f319 (@lcvelylilith) February 20, 2020
Before I begin, it might be worth explaining the Malay conception of the spirit world. At its deepest level, Malay religious belief is animist. All living beings and even certain objects are said to have a soul. Natural phenomena are either controlled by or personified as spirits
Although these beings had to be respected, not all of them were powerful enough to be considered gods. Offerings would be made to the spirits that had greater influence on human life. Spells and incantations would invoke their
Animist ceremonies of a religious or magical nature were normally held for the purpose of divination or making a request. This would either be done at a keramat or at a shrine similar to the Thai spirit houses or Chinese roadside shrines pic.twitter.com/I1hliyi0x3
— \u2745\u1710\u170b\u1713\u170e (@uglyluhan) June 16, 2019
Two known examples of such elemental spirits that had god-like status are Raja Angin (king of the wind) and Mambang Tali Arus (spirit of river currents). There were undoubtedly many more which have been lost to time
Contact with ancient India brought the influence of Hinduism and Buddhism to SEA. What we now call Hinduism similarly developed in India out of native animism and the more formal Vedic tradition. This can be seen in the multitude of sacred animals and location-specific Hindu gods
