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.
More from Arthouse-Kuklite
More from Maths
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
You May Also Like
Following @BAUDEGS I have experienced hateful and propagandist tweets time after time. I have been shocked that an academic community would be so reckless with their publications. So I did some research.
The question is:
Is this an official account for Bahcesehir Uni (Bau)?
Bahcesehir Uni, BAU has an official website https://t.co/ztzX6uj34V which links to their social media, leading to their Twitter account @Bahcesehir
BAU’s official Twitter account
BAU has many departments, which all have separate accounts. Nowhere among them did I find @BAUDEGS
@BAUOrganization @ApplyBAU @adayBAU @BAUAlumniCenter @bahcesehirfbe @baufens @CyprusBau @bauiisbf @bauglobal @bahcesehirebe @BAUintBatumi @BAUiletisim @BAUSaglik @bauebf @TIPBAU
Nowhere among them was @BAUDEGS to find
The question is:
Is this an official account for Bahcesehir Uni (Bau)?
Bahcesehir Uni, BAU has an official website https://t.co/ztzX6uj34V which links to their social media, leading to their Twitter account @Bahcesehir
BAU’s official Twitter account
BAU has many departments, which all have separate accounts. Nowhere among them did I find @BAUDEGS
@BAUOrganization @ApplyBAU @adayBAU @BAUAlumniCenter @bahcesehirfbe @baufens @CyprusBau @bauiisbf @bauglobal @bahcesehirebe @BAUintBatumi @BAUiletisim @BAUSaglik @bauebf @TIPBAU
Nowhere among them was @BAUDEGS to find