In this lesson, we will review the definition of the reflexive property of equality. We will also look at why this property is important. Following the lesson will be a brief quiz to test your knowledge on the reflexive property of equality.
Defining the Reflexive Property of Equality
If you look in a mirror, what do you see? Your reflection! You are seeing an image of yourself. You could look at the reflexive property of equality as when a number looks across an equal sign and sees a mirror image of itself! Reflexive pretty much means something relating to itself.

The reflexive property of equality simply states that a value is equal to itself. Further, this property states that for all real numbers, x = x. What is a real number, though?

Real numbers include all the numbers on a number line. They include rational numbers and irrational numbers. A rational number is any number that can be written as a fraction. An irrational number, on the other hand, is a real number that cannot be written as a simple fraction. Square roots would be in this category. In fact, real numbers pretty much entail every number possible except for negative square roots because they are imaginary numbers.

Therefore, the reflexive property of equality pretty much covers most values and numbers. Again, it states simply that any value or number is equal to itself.

Importance of the Reflexive Property of Equality
Why is the reflexive property of equality important or even necessary to state? After all, it seems so obvious! The reason is that if we don’t clearly make a statement of something in mathematics, how do we know that we all agree that it is true? Even for something so simple as the reflexive property of equality, we need to have a property so that we know that we all agree that x = x.

Also, if we did not have the reflexive property of equality, how would we explain that x x is not true? Because of this property of equality, we can affirm that statements like x < x are false.

Examples
Here are some examples of the reflexive property of equality:

x = x

y = y

x + y = x + y

1 = 1

1/2 = 1/2

432 = 432

46 + 56 = 46 + 56

2x + y = 2x + y

4.789 = 4.789

6^2 = 6^2

What is the ‘White Man’s Burden?’ You may be familiar with the phrase, but unaware that it comes from a poem written by Rudyard Kipling. This lesson will discuss the meaning and the importance of that poem.
Background on Kipling, Imperialism
The United States is used to exerting its influence and power, but just over 100 years ago, this was not the case. During the 19th century, the United States followed a policy of isolationism; as a country, it did its best to stay out of the business and conflicts of other countries, and it encouraged other countries to keep their noses out of U.S. business as well.

During that same time, Great Britain controlled a massive empire. While the United States was still an isolationist country, European powers embraced imperialism, a foreign policy where the country expanded its influence around the world, both peacefully and by force. They scrambled to control as much of the world as they could. India was considered to be the crown jewel of the British Empire, but maintaining that jewel came at a high price.

Rudyard Kipling was born in 1865 in Bombay. He spent his early life in India, but went to school in England before returning to his birthplace in the 1880s. Kipling would become a famous poet and novelist whose work was heavily influenced by his unique perspective. Kipling witnessed firsthand the number of British and Indian lives that were lost as a result of imperialism. Despite this fact, Kipling believed that the British not only had a right to control India, but also had the responsibility of civilizing the Indian people. This sentiment was reflected in his poem, ‘The White Man’s Burden’.

‘The White Man’s Burden’
Kipling’s poem ‘The White Man’s Burden’ was originally published in February of 1899, under the title, ‘An Address to the United States’.

But why would a British writer publish a poem specifically for the United States? In 1898, the United States went to war with Spain as a result of a revolution in Cuba. On the surface, it looked like the United States merely wanted to help Cuba gain its independence from Spain. But by the end of the Spanish-American War, this was obviously not the case. As the winner of the war, the United States controlled the Cuban government and also walked away with the rights to Puerto Rico, Guam, and the Philippines. After decades of isolationism, the United States had finally become an imperialist country.

‘The White Man’s Burden’ was meant to both encourage and warn the United States. In Kipling’s view, imperialism was not just a way for countries to grab power; it was also a form of humanitarianism, a way to help less fortunate people around the world. Kipling’s poem explained that as an advanced nation, the United States was responsible for educating and civilizing the native peoples it now controlled. This responsibility was the White Man’s burden.

The phrase White Man can be taken two different ways. Literally, the White Man describes people who are Caucasian. In the early 20th century, many Americans believed in the concept of social Darwinism, where certain people were superior to others based on their color and race. The phrase White Man can also be taken figuratively. Around the time the poem was published, people who were considered to be good or pure were called White Men.

Although Kipling’s poem emphasized the goodness of imperialism and the White Man’s burden, he also told the United States that this burden came with a price. The native people they ruled over would be resistant. Controlling and civilizing these places would also require significant manpower and, in many instances, would lead to deaths.

This lesson focuses on ribosomal RNA (rRNA). It will cover what rRNA is, what it does in our cells, and how it is made. At the end of the lesson is a short description of how rRNA is used in medicine and science.
What Is rRNA?
To begin, ribonucleic acids (RNA) are a group of large molecules that have many different roles. They are especially important in the coding, decoding, regulation, and expression of our genes. As the name implies, ribosomal RNA (rRNA) is part of the ribosome. A ribosome is the protein builder of the cell. The rest of a ribosome is made up of proteins. In addition, there are two rRNA in each ribosome, one in the large subunit and one in the small subunit.

Function
Translation is the name of the process our cells use to make proteins. Ribosomes are the organelles that can take a copy of our genetic material and translate it into a protein. The original genetic material is DNA, and it is stored in the cell’s nucleus. When a specific protein is needed, our cells make a copy of the DNA. This copy is also RNA, but it is called messenger RNA, or mRNA. Thus, ribosomes translate mRNA into protein.

To make a protein, ribosomes link together amino acids. The mRNA has the specific order in which the amino acids must be joined, and each protein has a different order of amino acids. The small subunit of rRNA can read the order of amino acids. Linking amino acids together is the function of the rRNA in the large subunit of the ribosome.

Sequence
rRNA Subnits
table of components of rRNA subunits
The sequence of rRNA is highly complex and derived from multiple genes. The table summarizes the components of the large and small subunit rRNA. Sedimentation rate (S) of the subunit is affected by the size of each subunit. As you can see, the large subunit of rRNA is made of two smaller pieces, while the small subunit is only one piece. The structure of the small subunit of eukaryotic rRNA has been discovered.

Synthesis
All RNA molecules are created by transcription, or making a copy of DNA. The protein that makes a copy of DNA is RNA polymerase. This protein is an enzyme that can read DNA and make an RNA copy. Transcription starts when the RNA polymerase enzyme binds DNA at a specific location called a promoter. Promoters are found ‘upstream’ of a gene. RNA polymerase reads the DNA in only one direction and continues reading and creating RNA until it reaches the end of the gene. The end of the gene has a special region called a stop codon. This region literally signals the RNA polymerase enzyme to stop copying the DNA.

Importance
Ribosomal RNA characteristics are important in medicine. Both prokaryotes (single-celled organisms, like bacteria) and eukaryotes (organisms whose cells have a nucleus and organelles, like the cells in our bodies) have ribosomes with rRNA. Prokaryotes and eukaryotes differ in the size and sequence of the rRNA in each subunit. Modern medicine exploits this difference using antibiotics. Therefore, rRNA is the target of several antibiotics, including chloramphenicol, erythromycin, and streptomycin.

Simple cuboidal epithelium is a type of tissue that is found lining parts of organs and ducts in the body. Its structure allows for absorption and diffusion in those areas. Learn more about this tissue and quiz yourself at the end of the lesson.
What is Epithelium?
Our bodies are complex machines made up of many different parts and systems. On a large scale, we could say that we are made up of two arms, two legs, a torso, and a head. But that is not a very specific or scientific description. It would be much more fitting to say that our body is made up of different types of tissue. Human body tissue is composed of groups of cells with a similar structure and function. Different sets of tissue make up organs and other parts of the body.

In this lesson, we will be looking at a type of tissue called epithelium. Epithelium provides both a protective covering for our body as well as a lining for internal areas. For example, our outer layer of skin, as well as the lining of our mouths, are made of epithelial tissue. There are many types of epithelial tissue, and in this lesson we will be examining one known as simple cuboidal epithelium.

Various Types of Epithelium
Types of Epithelium
Structure of Simple Cuboidal Epithelium
Let’s zoom in on this tissue to gain a better understanding of what its name means. We have already defined epithelium as a type of tissue that covers and lines body parts. When we add the word simple, this indicates that it is made up of only one layer of cells. Some types of epithelium have multiple layers, depending on their function. But simple cuboidal epithelium is just one layer thick.

The cells in epithelial tissue are joined very tightly together to essentially form a sheet. Because usually epithelium acts as a protective barrier or lining, this tissue must be a tightly-knit layer. Imagine rolling out a pie crust that you will lay into a pie plate. You want it to be a smooth sheet, with no holes or gaps so that it makes a continuous lining for the pie. It’s a similar concept with epithelial tissue.

Now what about the word cuboidal? You may already have a guess as to what this says about these cells. Each cell is, in fact, shaped like a cube. It is as wide as it is tall. If you can picture dice, you can understand what these cells look like. So now that we’ve defined each term in this rather long name, let’s put them together visually to better understand this tissue.

Basic Structure of Simple Cuboidal Epithelium
Simple cuboidal epithelium
To create a visual representation of simple cuboidal epithelium, imagine you have a bag of dice. Each die represents a cuboidal cell. You will now begin to line the dice up, with each closely touching the next. You make row after row, each touching the next with no gaps in between. When you’re finished, you have a single layer of dice that is several rows wide, representing a sheet of simple cuboidal epithelium.

Function and Location of Simple Cuboidal Epithelium
Now you probably haven’t spent much time thinking about simple cuboidal epithelium, because it’s not a type of tissue that we can see; most of us probably aren’t aware that it exists. That’s because it is found hidden deep inside our bodies in places such as the lining of kidney tubules and walls of respiratory bronchioles.

In this lesson, you will learn about the satellite nations of the Cold War. Explore how they became satellites, how the Soviet Unions kept its control over them during the Cold War, and how they eventually regained independence.
Definition
When you think of a satellite, you might think about the structure that beams down signals from space to help you get all the TV channels you want. Satellites are launched into orbit over Earth, and held in place by the earth’s gravity. So, how can a nation be like a satellite? When we talk about a satellite nation, we are talking about a nation that is aligned with and under the influence of another nation. It is caught in the orbit of the other country, just like a satellite is caught in the orbit of a planet.

The term satellite nation was first used to describe certain nations in the Cold War. These were nations that were aligned with, but also under the influence and pressure of, the Soviet Union. The satellite nations of the Cold War were Poland, Czechoslovakia, Hungary, Romania, Bulgaria, and East Germany. Countries in the West (like the U.S.) began using the term ‘satellite nation’ to describe these countries, because they were held in the orbit by the gravitational pull of the Soviet Union.

The Road to Satellite Nation
So, how did these countries come to be satellites of the Soviet Union? Many of them had long historical relations with Russia due to their geographical proximity and were established well before World War II. Worried about aggressive German expansion, many Eastern European countries looked to their bigger neighbor, the Soviet Union, to protect them.

It wasn’t until WWII that the satellites drew closer to the Soviet Union. Nazi Germany swept through Eastern Europe, conquering every country in their path before trying to defeat the Soviet Union. At the 1942 Battle of Stalingrad, the Soviets were able to stop the Germans, eventually pushing them all the way back to Berlin. Soviet forces liberated Eastern Europe along the way, and kept troops stationed in these countries. By the end of the war, the Soviet Union controlled most of Eastern Europe.

At the 1945 Yalta Conference, the leaders of the United States, England, and the USSR discussed what the post-war world should look like. The Soviet leader, Joseph Stalin, argued that the Soviet Union should take the lead in rebuilding and assisting Eastern European countries like Poland. He promised to honor free elections and to let these countries determine their own futures. In reality, though, Stalin intended to maintain control over the Eastern European countries to create a kind of protective zone against future invasions from the west.

The Allies agreed to Stalin’s plan, unaware of his true intentions. With Soviet troops still occupying these Eastern European countries, Moscow sent in agents with instructions to rig elections to ensure that pro-Soviet communist governments won. These countries would look independent, but would be totally tied to the Soviet Union.

Satellite Nations During the Cold War
Very soon after WWII, it became clear that the communist Soviet Union and capitalist United States would clash. Each side wanted to show strength and power. It became more important for the Soviet Union to keep its satellite nations under its control, so it created three organizations to bind the satellites together politically, economically, and militarily.

In 1947, the Soviet Union organized Cominform, the Communist Information Bureau. Cominform enforced ideological and political conformity under the direction of Moscow. As Europe struggled toward economic recovery after the war, the United States initiated the Marshall Plan, which promised aid to any country that applied for help. Worried that some Eastern European countries might look to the U.S. for help, the Soviet Union responded by creating Comecon in 1949. Comecon promised economic aid to its members and kept the economies of the satellites tied to the command economy of the Soviet Union.