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by lpetrich
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45

### 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...

by lpetrich
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4
Views
45

### 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 =...

by lpetrich
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4
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45

### 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.
...

by lpetrich
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4
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45

### 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...

by lpetrich
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7
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75

### 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

Substitute into the integrand: x^2+3*y = r^2*cos(a)^2 + 3*(r*sin(a) +...
6. ## Thread: US rent moratorium expired

by lpetrich
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13
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155

### 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...
7. ## Thread: US rent moratorium expired

by lpetrich
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13
Views
155

### 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...
8. ## Thread: Billionaires Blast off

by lpetrich
Replies
463
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5,985

### 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...
9. ## Thread: Democrats trying to unseat each other II

by lpetrich
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122
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5,440

### 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 -...
10. ## Thread: Democrats trying to unseat each other II

by lpetrich
Replies
122
Views
5,440

### 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...
11. ## Thread: Democrats trying to unseat each other II

by lpetrich
Replies
122
Views
5,440

### 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. ## Thread: Natural numbers vs. whole numbers vs. integers

by lpetrich
Replies
7
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78

### 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. ## Thread: How many groups and semigroups and rings and the like - abstract algebra

by lpetrich
Replies
67
Views
1,359

### 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. ## Thread: How many groups and semigroups and rings and the like - abstract algebra

by lpetrich
Replies
67
Views
1,359

### 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...
15. ## Thread: Billionaires Blast off

by lpetrich
Replies
463
Views
5,985

### Define "market".

Define "market".
16. ## Thread: Now the Coup Starts

by lpetrich
Replies
1,973
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113,450

### 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. ## Thread: How many groups and semigroups and rings and the like - abstract algebra

by lpetrich
Replies
67
Views
1,359

### 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. ## Thread: How many groups and semigroups and rings and the like - abstract algebra

by lpetrich
Replies
67
Views
1,359

### 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. ## Thread: How many groups and semigroups and rings and the like - abstract algebra

by lpetrich
Replies
67
Views
1,359

### 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. ## Thread: How many groups and semigroups and rings and the like - abstract algebra

by lpetrich
Replies
67
Views
1,359

### 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"...

by lpetrich
Replies
2,461
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96,950

### 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. ## Thread: How many groups and semigroups and rings and the like - abstract algebra

by lpetrich
Replies
67
Views
1,359

### 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. ## Thread: How many groups and semigroups and rings and the like - abstract algebra

by lpetrich
Replies
67
Views
1,359

### 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. ## Thread: How many groups and semigroups and rings and the like - abstract algebra

by lpetrich
Replies
67
Views
1,359

### 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. ## Thread: Natural numbers vs. whole numbers vs. integers

by lpetrich
Replies
7
Views
78

### 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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