OpenLLM-France/wikimedia huggingface dataset:
# Math for Non-Geeks/ Proving discontinuity
## Overview

Recall that whenever we want to prove the negation of a statement about some elements of a set, we need to show that there as at least one element in that set for which the statement is not true. So, in order the prove the discontinuity of a function, all you have to show is that the function has (at least) one point of discontinuity. There are several methods available for proving the existence of a point of discontinuity:
* Sequence criterion: Show that the function doesn't fulfill the sequence criterion at one particular point
* Considering the left- and right-sided limits: Calculate the left-sided and right-sided limits of the function at a particular point. If either one of these limits doesn't exist, or if the limits are different, then the function is discontinuous at that point.
* Epsilon-Delta Criterion: Show that the function doesn't fulfill the epsilon-delta criterion at a particular point.

## Sequence Criterion

‌

### Review: Sequence Criterion

Math for Non-Geeks: Sequential definition of continuity

### Sketch of the proof

Math for Non-Geeks: Sequential definition of continuity

### Example exercises

Math for Non-Geeks: Sequential definition of continuity

## Epsilon-Delta Criterion

‌

### Review: Epsilon-Delta Criterion

Math for Non-Geeks: Epsilon-delta definition of continuity

### General proof structure

The Epsilon-Delta criterion of discontinuity can be formulated in predicate logic as follows:
${\color {Red}\exists \epsilon >0}\ {\color {RedOrange}\forall \delta >0}\ {\color {OliveGreen}\exists x\in D}:{\color {DarkOrchid}|x-x_{0}|<\delta }\land {\color {Blue}|f(x)-f(x_{0})|\geq \epsilon }$
From here we get a schematic that allows us the prove the discontinuity of a function using the delta-epsilon criterion:
${\begin{array}{l}{\color {Red}\underbrace {{\underset}{\text{Choose }}\epsilon =\ldots } _{\exists \epsilon >0}}\ {\color {RedOrange}\underbrace {{\underset}{\text{Let }}\delta >0{\text{ beliebig.}}} _{\forall \delta >0}}\\{\color {OliveGreen}\underbrace {{\underset}{\text{Choose }}x=\ldots {\text{ Es ist }}x\in D{\text{, weil}}\ldots } _{\exists x\in D}}\\{\color {Black}{\text{We have:}}}\\[0.5em]\quad \quad {\color {DarkOrchid}{\text{Proof for }}|x-x_{0}|<\delta }\\[0.5em]\quad \quad {\color {Blue}{\text{Proof for }}|f(x)-f(x_{0})|\geq \epsilon }\end{array}}$

### Example exercise

Math for Non-Geeks: Epsilon-delta definition of continuity

## Exercises
### Epsilon-delta criterion: Signum function

Math for Non-Geeks: Epsilon-delta definition of continuity
# Math for Non-Geeks/ Exercises: Convergence criteria for series
## Application of convergence criteria

Math for Non-Geeks: Template:Aufgabe
Math for Non-Geeks: Template:Aufgabe
Math for Non-Geeks: Template:Aufgabe
Math for Non-Geeks: Template:Aufgabe

## Term test - strengthened version

Math for Non-Geeks: Template:Aufgabe

## Cauchy criterion: an application

Math for Non-Geeks: Template:Aufgabe

## Root and ratio test: estimate of errors

In some cases, the infinite sum $s=\sum _{k=1}^{\infty }a_{k}$ cannot be computed explicitly. We can try to approximate it by $s_{n}=\sum _{k=1}^{n}a_{k}$. The following exercises are devoted to giving upper bounds on the approximation error $|s-s_{n}|$:
Math for Non-Geeks: Template:Aufgabe
Math for Non-Geeks: Template:Aufgabe
Math for Non-Geeks: Template:Aufgabe

## Alternating series test with error bounds

Math for Non-Geeks: Template:Aufgabe

## Cauchy condensation test

Math for Non-Geeks: Template:Aufgabe

## Further convergence criteria

Math for Non-Geeks: Template:Aufgabe
Math for Non-Geeks: Template:Aufgabe
# Drugs: Fact and Fiction

Disclaimer Notice: Recreational and enhancement drug use can be dangerous and is often illegal. Before reading this book, make sure you understand Wikibooks' medical, legal and risk disclaimers. Information gathered in these pages is for informational purposes only.

## Table of contents

* Introduction
* General Drug Information
* Hallucinogens
* Stimulants
* Depressants
# Drugs: Fact and Fiction/2C

The 2C drugs include 2-CI and 2-CT-7. The majority of these chemicals were discovered by Alexander Shulgin, who published his findings in the book PiHKAL.
# Drugs: Fact and Fiction/Adderal

Dosages: 20–100 mg
20 mg: Slightly tweaked, more energy, willingness to work. 50 mg & up: extremely tweaked, endless energy, unstoppable urge to be productive, very concentrated.
Side effects: Dry mouth, increased sweating, teeth grinding, insomnia, diarrhea, shrunken penis, inability to obtain an erection.
# Drugs: Fact and Fiction/Caffeine

Caffeine occurs naturally in the seeds and leaves of many plants, including coffee and tea. It is often added to sodas and energy drinks. It is also sold as a non-prescription drug to aid wakefulness. Effects include loss of fatigue, loss of appetite, mild euphoria, and increased urination.
Sensitivity to caffeine varies depending on the individual.
While caffeine is addictive, withdrawal symptoms are usually mild, and pass after a few days. Symptoms of withdrawal include headaches, fatigue, loss of concentration, and, in some cases, mild depression.
# Drugs: Fact and Fiction/Cocaine
## What does Cocaine do to you?

Taking cocaine makes users feel on top of the world. Its effect is like the stimulant ‘amphetamines’ (speed) but is stronger and doesn't last as long. People taking it feel wide-awake, confident and on top of their game.
Cocaine is a stimulant, so it can raise the body’s temperature, make the heart beat faster and stave off feelings of hunger.
The effects of crack smoking are virtually immediate, peaking for about two minutes and lasting for only about 10 minutes. For snorted coke there is a slower time to peak but the effects still don’t last that long (around 20-30 minutes).
It also makes you think/see things that are not there.
# Drugs: Fact and Fiction/DXM
## What Is DXM?

DXM is the active ingredient found in over the counter cough and cold medications. When taken in recommended doses, these medications are safe and effective.

## Health and Safety

In very large quantities, DXM can cause effects similar to those of ketamine and PCP because these drugs affect similar sites in the brain. These effects can include impaired motor function, numbness, nausea/vomiting, and increased heart rate and blood pressure. On rare occasions, hypoxic brain damage—caused by severe respiratory depression and a lack of oxygen to the brain—has occurred due to the combination of DXM with decongestants often found in the medication.
NOTE! Abuse of cough medicine has more serious side effects then those listed here. The amount of cough syrup which contains "recreational" dose of DXM can have a fatal dosage of its other active ingrediates.
# Drugs: Fact and Fiction/Depressants
### Depressants
#### Barbiturates

* Butalbital (Fioricet)

#### Benzodiazepines

* Alprazolam (Xanax)
* Diazepam (Valium)
* Lorazepam (Ativan)
* Clonazepam (Klonopin & Rivotril)
Nitrazepam(Mogadon) Temazepam loprazolam

#### Sedative Hypnotics

* Alcohol
* Chloral Hydrate
* Gamma-Hydroxybutyrate (GHB)
* Zolpidem (Ambien)
* Zopiclone (Lunesta)

#### Narcotics (Opioids)

* Opium
* Codeine
* Morphine
* Oxycodone
* Hydrocodone
* Diamorphine (Heroin)
* Hydromorphone (Dilaudid)
* Fentanyl
# Drugs: Fact and Fiction/Amphetamine

Amphetamines are artificially made stimulants and prescription drugs like concerta. Amphetamines were first made in Germany as treatment for asthma (20th century). Some "street" names for ampetamines are uppers, ups, speed, black beauties, and wake ups. Amphetamines can be inhaled, injected, or most comonly swallowed. Effects on the body are high energy and feelings of well being.
# Drugs: Fact and Fiction/Depressants/Zolpidem (Ambien)

One of the most popular prescription sedative-hypnotics, zolpidem, commonly known as Ambien is used as a sleep aid. At prescribed doses, the patient will notice drowsiness within 20-60 minutes within consumption of dose.
Prescription doses of zolpidem include:
Ambien
* 5 mg
* 10 mg
Ambien CR (Time-Release version)
* 6.25 mg
* 12.5 mg
How Zolpidem Works
Zolpidem works by binding preferentially to the omega-1 (BZ-1) receptor subtype of the GABAA receptor complex. This subtype is thought to be the one most closely associated with sleep.
In contrast, benzodiazepines do not have a receptor preference, so they bind to—and activate—all omega (BZ) receptor subtypes. Other omega (BZ) receptor subtypes are associated with anxiolytic, myorelaxant, and anticonvulsant activity.
As Described on Ambien.com
# Drugs: Fact and Fiction/Hydrocodone

Hydrocodone is a popular pain-relief medication. Common prescription names are Vicodin, Lortab, and Vicoprofen. Prescribed for pain relief, hydrocodone is much like codeine, an opiate agonist, analgesic and antitussive used in the treatment of mild to moderate pain.
Prescription doses of hydrocodone include:
Vicodin
(Hydrocodone/Acetaminophen)
* 5/500 mg
* 7.5/750 mg
* 10/660 mg
Generic and/or Lortab
(Hydrocodone/Acetaminophen)
* 2.5 mg/500 mg
* 5 mg/500 mg
* 7.5 mg/325 mg
* 7.5 mg/500 mg
* 7.5 mg/650 mg
* 7.5 mg/750 mg
* 10 mg/325 mg
* 10 mg/500 mg
* 10 mg/650 mg
* 10 mg/660 mg
* 10 mg/750 mg
Liquid "Elixir" Hydrocodone
For people who may have trouble swallowing due to throat/tonsil surgery, or who may have heavy congestion of musus either Lortab Elixir, Atuss HX, Cotuss-V, Entuss, or Vortex are prescribed for pain relief and/or moderate to severe congestion from flu or similar illnesses. Liquid hydrocodone syrups commonly contain guaifenesin and hydrocodone.
# Drugs: Fact and Fiction/Introduction
## Introduction

What is a drug? Why do people take drugs? What are the effects drugs have on the body? This book will serve to answer questions, give facts, and dispel persistent rumors spread about drugs. First we need to describe what the word "drugs" refers to.

## What are drugs?

Colloquially, drugs often refer to illicit drugs. More broadly, a drug is any chemical substance that, when absorbed into the body of a living organism, alters normal bodily function. Of course this covers all medical drugs, from aspirin and penicillin to heroin and arsenic.
This book will focus on primarily drugs used outside of medical need. These are, generally speaking, psychoactive drugs which taken for any other reason than medical benefit.
Recreational drug use is the use of chemical substances for enjoyment or entertainment purposes. Due to lack of cultural background, weak social support, technological alteration of natural occurring compounds for potency or profit and no control about product quality, consumer age limits or mental state, this practice can be extremely dangerous, leading to death, damage to self and dependency.
Religious drug use is the use of chemical substances in religious rites or with religious connotations, practiced by Native-Americans and South American tribes. Due to the high level of understanding and experience, these culture have in handling the naturally occurring compounds, there is a low risk involved, some of the practices can even aid in correcting dependencies on other substances.
Cultural and creative use due the effect of some of the drugs in brain chemistry some people rely in drugs to augment creative capability and establish new paths for problem solving and self understanding. Can lead to drug abuse and dependency.
Functional use some drugs are used to temporarily or permanently alter physical or mental limitations. This can also lead to drug abuse and dependency.
Notice that we do not use the term "illegal drug". There are several reasons for this. First the definition of what is legal varies from country to country. Secondly some drugs that are abused, taken at levels beyond the recommended dosages, or even prescribed medically or sold over the counter lead to addiction and are legal drugs. Drug use is generally regulated for the safety of the public, but the exact legal status of any substance is dependent on country and/or jurisdiction and political and religions positions.
* A psychoactive drug is any substance that alters your perception or senses.
* A addiction causing drug is any substance that creates physical or psychological dependency in its use.
# Drugs: Fact and Fiction/Khat

Khat is catha edulis, a flowering evergreen shrub. The leaves, twigs, and shoots are chewed fresh, or dried and made into tea or smoked. Khat leaves contain alkaloids called cathine and cathinone. The main responsible of the psychostimulants effects is cathinone, similar in pharmacological activity and structure to amphetamine but is 2-to-10 fold less active. Effects include euphoria, loss of appetite, reduction in fatigue, and increased heart rate. Cathinone stimulates the central nervous system by releasing dopamine, inhibiting dopamine and norephinefrine reuptake, and affecting serotonin system.
Usage of in East-Africa and the southwestern of the Arabia Peninsula, in countries such as Somalia, Kenya, Djibuti or Ethiopia, and is strongly associated with Yemen.
It is illegal in the United States, but legal in The Netherlands and Great Britain.
# Drugs: Fact and Fiction/LD50

The LD/50 of any substance is the lethal dose amount – typically given in a milligrams of the substance per kilogram of the users weight (mg/Kg) – needed to cause death to 50% of users.
This of course is never tested on humans. Instead a drug is administered intravenously to rats.
The number is not very reliable for two major reasons: First of all, there is quite a difference between humans and rats. Humans have a completely different metabolism compared to our furry friends. This can either mean it takes more or less of a substance to reach LD/50, depending on the drug.
Secondly, many drugs are ingested orally. When something is absorbed by the GI track, it makes a pass through the liver. The liver breaks down a certain amount of the substance, usually into inactive chemicals. (Although sometimes the liver breaks down an inactive chemical into an active one, such as with Codeine.)
Wherever possible, this book includes the known human overdose threshold (which is often a good deal below the LD/50), and/or a safe dosage range to stay clear of any dangers.
# Drugs: Fact and Fiction/Kratom

Effects List
POSITIVE
NEUTRAL
NEGATIVE
The effects of Mitragyna speciosa are described as being a combination of both stimulation and sedation. The stimulatory effects may be shorter in duration than the sedation effect, coming on faster and fading sooner.
See Kratomplant pictures on this site Kratomplant pictures
# Drugs: Fact and Fiction/Meth

The effects of methamphetamine depend on the method of intake. If taken intravenously the effects are an extremely intense burning feeling throughout the body for approximately 15 minutes. These effects can come about from very small doses.
# Drugs: Fact and Fiction/Mushrooms

Psilocybin mushrooms, commonly known as magic mushrooms, are a polyphyletic informal group of fungi that contain psilocybin which turns into psilocin upon ingestion. Biological genera containing psilocybin mushrooms include Copelandia, Gymnopilus, Inocybe, Panaeolus, Pholiotina, Pluteus, and Psilocybe. Psilocybin mushrooms have been and continue to be used in indigenous New World cultures in religious, divinatory, or spiritual contexts. Psilocybin mushrooms are also used as recreational drugs. They may be depicted in Stone Age rock art in Africa and Europe, but are most famously represented in the Pre-Columbian sculptures and glyphs seen throughout North, Central and South America.
# Drugs: Fact and Fiction/Nicotine

Any of various drugs that inhibit, enhance, or mimic the action of the neurotransmitter acetylcholine, the primary transmitter of nerve impulses within the parasympathetic nervous system—i.e., that part of the autonomic nervous system that contracts smooth muscles, dilates blood vessels, increases bodily secretions, and slows the heart rate. Some cholinergic drugs, such as muscarine, pilocarpine, and arecoline, mimic the activity of acetylcholine in stimulating the parasympathetic nervous system. These drugs have few therapeutic uses, though one of them, nicotine, is the principal addictive ingredient in the tobacco used in cigarettes and cigars. Other cholinergic drugs, such as atropine and scopolamine, inhibit the action of acetylcholine and thus suppress all the actions of the parasympathetic nervous system. They are used therapeutically to diminish salivation and bronchial secretions during anesthesia and to dilate the pupil during ophthalmological procedures. Scopolamine is also used to treat motion sickness, an effect that depends on its ability to depress the activity of the central nervous system.
# Drugs: Fact and Fiction/Ritalin

Generic For: Methylphenidate

## Dose

* Light: 5-15 mg
* Common: 20-40 mg
* Strong: 50+ mg
Ritalin comes in 5, 10, 15, and 20 Mg doses. May come in an instant release but is more commonly found in XR (Extended Release) form.

## Duration
### From an XR capsule

* Come up: 1/2-1 hour
* Peak: 1 & 4 hours
* Come down/ After effects: Up to 24 hours

### From an instant release pill

* Come up: 20-40 Minutes
* Peak: 1-3 hours
* Come down/ After effects: Up to 24 hours
# Drugs: Fact and Fiction/Salvia

Salvia (Sage) is a common perennial herb that grows throughout the world. The plant grows to be several feet tall and has large light-green leaves. Salvia is a member of the mint family, and is considered a common garden plant. Most common forms of Salvia can be found in plant nurseries. They are not hallucinogenic and will only give users a headache if smoked.
Diviner's Sage, Salvia divinorum - commonly referred to as "salvia" - is one of the hundreds of species of the Salvia genus. It is not native to any place, although it is commonly grown in some parts of Mexico, and now grows wild in some parts of the Sierra Mazatec region.

## General

Although some users take salvia recreationally at a very low dosage, it is not a "party drug." Daniel Siebert, ethnobotanist and salvia advocate, remarks, "...salvia is not 'fun' in the way that alcohol or cannabis can be. If you try to party with salvia, you will probably not have a good experience."
The active chemical - salvinorin A - is the strongest naturally occurring psychoactive known to date. It has been used by natives for thousands of years to seek divine spiritual insight. The internet brought the plants psychoactive qualities to wider attention. In recent years several countries have introduced legislation to make prepared forms of the plant illegal. It remains legal in most of North America because of the lack of media attention, and the very small abuse potential. (See legality section below.)
There is no known lethal dosage of Salvia divinorum. However, it is very strongly recommended that a trip sitter be present. Because of its short-lasting effects (when smoked), users can take turns being a sitter.
Before setting forth to explore the potential of this substance, please read this entire page!

## Legality

This substance is illegal in Australia, Denmark, Finland, Norway, Sweden, Switzerland, Italy, Spain, Germany, Belgium and Brazil. It is legal in many other countries, including Austria, France, and has differing levels of legality/illegality in different states of the USA. As of 2017, it is illegal to possess, distribute, or sell Salvia in Kansas, Delaware, Florida, Tennessee, Texas, Illinois, Louisiana, Missouri, Montana, North Dakota, and Oklahoma. It is legal for individuals over the age of 21 to buy, possess and use in California, but requirements re: it's retailing demand diligent current research.

## Methods of Ingestion

Salvia can be ingested in several ways that produce varying effects. A large amount of leaves can be chewed thoroughly to produce light but long lasting effects. More common is to smoke prepared extracts where the salvinorin A has been concentrated to several (Five to twenty-five times) the natural amount by weight.
# BASIC Programming/Beginning BASIC/Control Structures/IF...THEN...ELSEIF...ELSE

The IF...THEN...ELSEIF...ELSE control statement allows identifying if a certain condition is true, and executes a block of code if it is the case.
In some implementations of BASIC (but permitted by most versions), the IF statement may need to be contained in one line. However, ELSEIF may not be available in this case, and there is no need for an explicit END IF:
This carries over into some implementations of BASIC where if the "IF...THEN" statement is followed by code on the same line then it is fully contained. That is, the compiler assumes the lines ends with "ENDIF", even if it is not stated. This is important when dealing with nested "IF...THEN" clauses:
The ELSE clause, while following the "IF 2<3" statement, is associated with the "IF X<2" statement, because the "IF 2<3" statement has a PRINT statement on the same line.
Let me give some more examples of "If...Then...Else" programs:
Q1)Input the age of a person and check whether he/she is voter or not?
Ans1)
Q2)Input the age of a person to check if he/she is a senior citizen or not a senior citizen?
Ans2)
# Blended Learning in K-12

This book,"Blended Learning in K-12", is an overview of the concept of "blended learning" and how it relates to the integration of technologies in the K-12 environment by Edumix partners.
* Introduction to Blended Learning in K-12 (Higgins, Forbes, Flannell)
** What is "Blended Learning"?
** The many names of Blended Learning
** Why is Blended Learning Important?
* Evolution of Blended Learning (Krones, Meeker, Vavouliotis)
* Types oof Blended Learning (Hall, Watson, Benish, Morrison)
** Multimedia and Virtual Internet Resources
** Classroom Websites
** Course Management Systems
** Synchronous and Asychronous Discussions
* Characteristics of Blended Learning (Ferratier,Cheifetz, Ro)
** General Comparisons in Blended Learning
** Pedagogical Models- blending constructivism, behaviorism and cognitivism
** Synchronous and asynchronous communication methods
* Blended Learning by Design (Day, Yunker, Uhls)
** Designing a Lesson
** Guiding Principles
** Success Tips
* Application of Blended Learning in K-12 (Darche, Reed, Leven, Heater)
** Blended Learning In Grades K-2
** Blended Learning in Grades 3-6
** Blended Learning In Grades 7-8
** Blended Learning in Grades 9-12
* References (please add your references using APA style)
# OCR A-Level Physics/The Newtonian World/Ideal gases

Mole: The SI unit of amount of substance. Each mole contains elementary entities
Assumptions:
* Gas contains a very large number of molecules which are in continuous random motion
* Volume of molecules is negligible compared to volume of container
* Collisions between molecules and the container are perfectly elastic
* Time of collision is negligible compared to time between collisions
* Electrostatic forces are negligible except during collisions
How a gas exerts pressure on walls of container:
* Particle collides with container wall and changes momentum
* Force of wall on particle is equal to rate of change of particle's momentum (N2L)
* Force of particle on wall is same magnitude but opposite direction (N3L)
* Pressure = Sum of all particle forces / area of wall