Common Core math was the pinnacle of their evil genius, and low-point of our complacency... It disrupted the minds of an entire generation on how even the most basic things work.
Readin', Writin', & Rithmatic
How far did they get? Let's see.
1895 8th Grade Final Exam, Kansas:
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
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THE MEANING, SIGNIFICANCE AND HISTORY OF SWASTIK
The Swastik is a geometrical figure and an ancient religious icon. Swastik has been Sanatan Dharma’s symbol of auspiciousness – mangalya since time immemorial.
The name swastika comes from Sanskrit (Devanagari: स्वस्तिक, pronounced: swastik) &denotes “conducive to wellbeing or auspicious”.
The word Swastik has a definite etymological origin in Sanskrit. It is derived from the roots su – meaning “well or auspicious” & as meaning “being”.
"सु अस्ति येन तत स्वस्तिकं"
Swastik is de symbol through which everything auspicios occurs
Scholars believe word’s origin in Vedas,known as Swasti mantra;
"🕉स्वस्ति ना इन्द्रो वृधश्रवाहा
स्वस्ति ना पूषा विश्ववेदाहा
स्वस्तिनास्तरक्ष्यो अरिश्तनेमिही
स्वस्तिनो बृहस्पतिर्दधातु"
It translates to," O famed Indra, redeem us. O Pusha, the beholder of all knowledge, redeem us. Redeem us O Garudji, of limitless speed and O Bruhaspati, redeem us".
SWASTIK’s COSMIC ORIGIN
The Swastika represents the living creation in the whole Cosmos.
Hindu astronomers divide the ecliptic circle of cosmos in 27 divisions called https://t.co/sLeuV1R2eQ this manner a cross forms in 4 directions in the celestial sky. At centre of this cross is Dhruva(Polestar). In a line from Dhruva, the stars known as Saptarishi can be observed.
The Swastik is a geometrical figure and an ancient religious icon. Swastik has been Sanatan Dharma’s symbol of auspiciousness – mangalya since time immemorial.
The name swastika comes from Sanskrit (Devanagari: स्वस्तिक, pronounced: swastik) &denotes “conducive to wellbeing or auspicious”.
The word Swastik has a definite etymological origin in Sanskrit. It is derived from the roots su – meaning “well or auspicious” & as meaning “being”.
"सु अस्ति येन तत स्वस्तिकं"
Swastik is de symbol through which everything auspicios occurs
Scholars believe word’s origin in Vedas,known as Swasti mantra;
"🕉स्वस्ति ना इन्द्रो वृधश्रवाहा
स्वस्ति ना पूषा विश्ववेदाहा
स्वस्तिनास्तरक्ष्यो अरिश्तनेमिही
स्वस्तिनो बृहस्पतिर्दधातु"
It translates to," O famed Indra, redeem us. O Pusha, the beholder of all knowledge, redeem us. Redeem us O Garudji, of limitless speed and O Bruhaspati, redeem us".
SWASTIK’s COSMIC ORIGIN
The Swastika represents the living creation in the whole Cosmos.
Hindu astronomers divide the ecliptic circle of cosmos in 27 divisions called https://t.co/sLeuV1R2eQ this manner a cross forms in 4 directions in the celestial sky. At centre of this cross is Dhruva(Polestar). In a line from Dhruva, the stars known as Saptarishi can be observed.
