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    Algorithms for Egyptian Fractions - Introduction...

    Algorithms for Egyptian Fractions - Introduction

    Methods Based on Approximation
    Conflict Resolution Methods
    Methods Based on the Binary Number System
    Continued Fraction Methods
    Reverse...
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    Egyptian fraction gives several reduction...

    Egyptian fraction gives several reduction algorithms. Here are some of those that fit the Rhind papyrus's numbers:

    A simple one for odd x is 2/x = 2/(x+1) + 2/x*(x+1))

    A fancier one is 2/x =...
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    There is an algorithm called the greedy...

    There is an algorithm called the greedy algorithm. It starts with a fraction x and finds the largest reciprocal not greater than it. 1/r. If x != 1/r, then it repeats the calculation with x - 1/r.
    ...
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    Egyptian fractions

    Ancient Egyptians liked to represent fractions as sums of reciprocals, though they sometimes used fractions like 2/3 and 3/4.

    Egyptian fraction
    Rhind Mathematical Papyrus ~ 1550 BCE
    Greedy...
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    I will do it. First, change to polar...

    I will do it.

    First, change to polar coordinates centered on the disk: x = r*cos(a), y = r*sin(a) + 1
    Radius: r, angle: a

    Substitute into the integrand: x^2+3*y = r^2*cos(a)^2 + 3*(r*sin(a) +...
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    The Eviction Moratorium Is Expiring. Yet the Vast...

    The Eviction Moratorium Is Expiring. Yet the Vast Majority of Rental Aid Still Hasn’t Been Spent. – Mother Jones - "More than 6 million American households are behind on rent payments."

    Eviction...
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    US rent moratorium expired

    U.S. COVID-19 eviction ban expires, leaving renters at risk | Reuters

    Not much to landlords either.

    President Biden and the House and Senate Democratic leadership made themselves seem very...
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    So you want government military and police forces...

    So you want government military and police forces to be shut down?

    If governments cannot possibly do a good job at anything, then why trust governments with one's protection?

    Especially when...
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    Warrensville Heights Councilman Switches...

    Warrensville Heights Councilman Switches Endorsement from Shontel Brown to Nina Turner, Invites Other to Do the Same | Scene and Heard: Scene's News Blog

    The Meaning and History of First Names -...
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    Alexandria Ocasio-Cortez on Twitter: "What’s up...

    Alexandria Ocasio-Cortez on Twitter: "What’s up Cleveland! Thank you for the warm welcome! 💪🏽💙

    Are you ready to lace up your shoes and start knocking doors for @ninaturner?

    I’ll be helping...
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    Marisa Nahem on Twitter: "🚨NEWS: Rep....

    Marisa Nahem on Twitter: "🚨NEWS: Rep. @jamie_raskin announces endorsement of @ninaturner saying,

    “I see two kinds of politicians in Washington—justice politicians and power politicians. Nina...
  12. You're not missing anything. Addition and...

    You're not missing anything. Addition and subtraction are easy to picture on a numberline. Multiplication by an integer can be understood as repeated addition or subtraction, and division by a...
  13. Semilattice Semi-lattice - Encyclopedia of...

    Semilattice
    Semi-lattice - Encyclopedia of Mathematics

    That's related to:

    Lattice (order)
    Lattice - Encyclopedia of Mathematics

    A lattice is defined on a partially ordered set or poset....
  14. We have counts of nil-2 semigroups -- 1 -- and of...

    We have counts of nil-2 semigroups -- 1 -- and of nil-3 semigroups, and they seem to be nearly all semigroups. But what of the remainder?

    Groups are a subset of monoids, and most monoids are...
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    Define "market".

    Define "market".
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    McCarthy mocks Cheney and Kinzinger as 'Pelosi...

    McCarthy mocks Cheney and Kinzinger as 'Pelosi Republicans' | TheHill

    ‘Childish’: Kinzinger, Cheney Fire Back at McCarthy Calling Them ‘Pelosi Republicans’
  17. Then this document gets into "regular...

    Then this document gets into "regular semigroups". A semigroup element a is regular if there exists some x such that a = a*x*a. x need not be unique. If all a semigroup's elements are regular, then...
  18. That document mentions the "Rees matrix...

    That document mentions the "Rees matrix semigroups" - all finite zero-simple semigroups and some infinite ones have that form. Their construction is a bit complicated. Consider group G, sets I, U,...
  19. There's a result called Green's theorem, one that...

    There's a result called Green's theorem, one that can find us the subgroups that a semigroup contains. Not just semigroups but full-scale groups.

    If a H a^2 or H(a) = H(a^2) then a is the identity...
  20. Now to ideals of semigroups. For semigroup S,...

    Now to ideals of semigroups.
    For semigroup S,
    Left ideal: S*J <= J
    Right ideal: J*S <= J
    Two-sided (plain) ideal: union(S*J,J*S) <= J

    S itself is an ideal, the trivial ideal, and S is "simple"...
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    I took that test - Great British Intelligence...

    I took that test - Great British Intelligence Test - some things I did well on, some things not so well.
  22. About idempotence, every semigroup element can be...

    About idempotence, every semigroup element can be idempotent, but only one group element can be: the identity.

    Let us see what happens to a ring when all its elements are idempotent. That makes it...
  23. Another one we may call the maximum semigroup....

    Another one we may call the maximum semigroup. Consider a set S of completely ordered entities like real numbers or their subsets. Use operation

    a*b = max(a,b)

    It is a semigroup with identity...
  24. About semigroups, I've found Semigroup Theory: A...

    About semigroups, I've found Semigroup Theory: A Lecture Course by Victoria Gould. It gets arcane rather quickly, but it starts out with some examples of semigroups in addition to what's in Semigroup...
  25. Fractions? Their name comes from a Latin word for...

    Fractions? Their name comes from a Latin word for breaking, because fractions are amounts of broken-apart entities instead of complete ones. Like 1/2 for half of something.

    Rational numbers? They...
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