Immunology is a science that examines the structure and function of the immune system. It originates from medicine and early studies on the causes of immunity to disease. The earliest known mention of immunity was during the plague of Athens in 430 BC. Thucydides (460–395 BC) noted that people who had recovered from a previous bout of some diseases could nurse the sick without contracting the illness a second time.
In the 18th century, Pierre-Louis Moreau de Maupertuis made experiments with scorpion venom and observed that certain dogs and mice were immune to this venom. This and other observations of acquired immunity led to Louis Pasteur (1822–1895) developing vaccination and the germ theory of disease. Pasteur's theory was in direct opposition to contemporary theories of disease, such as the miasma theory. It was not until the proofs Robert Koch (1843–1910) published in 1891 (for which he was awarded a Nobel Prize in 1905) that microorganisms were confirmed as the cause of infectious disease. Viruses were confirmed as human pathogens in 1901, when the yellow fever virus was discovered by Walter Reed (1851–1902).
Immunology made a great advance towards the end of the 19th century, through rapid developments, in the study of humoral immunity and cellular immunity. Particularly important was the work of Paul Ehrlich (1854–1915), who proposed the side-chain theory to explain the specificity of the antigen-antibody reaction. The Nobel Prize for 1908 was jointly awarded to Ehrlich and the founder of cellular immunology, Ilya Mechnikov (1845–1916).
The simplest form of immunity is the DNA restriction system in bacteria that prevents infection by bacteriophages.
Infinity
Infinity is about things that never end.
Sometimes, it is also written formula_1. Infinity means many different things, depending on when it is used. The word is from Latin origin, meaning "without end". Infinity goes on forever, so sometimes space, numbers, and other things are said to be 'infinite', because they never come to a stop.
Infinity is usually not an actual number, but it is sometimes used as one. Infinity often says how "many" there is of something, instead of how "big" something is. For example, there are infinitely many whole numbers (called integers), but there is no integer which is infinitely big. But different kinds of math have different kinds of infinity. So its meaning often changes.
There are two kinds of infinity: potential infinity and actual infinity. Potential infinity is a process that never stops. For example, adding 10 to a number. No matter how many times 10 is added, 10 more can still be added. Actual infinity, on the other hand, refers to objects that are accepted as infinite entities (such as transfinite numbers).
Mathematicians have different sizes of infinity and three different kinds of infinity.
The number of things, beginning with 0, 1, 2, 3, ..., to include infinite cardinal numbers. There are many different cardinal numbers. Infinity can be defined in one of two ways: Infinity is a number so big that a part of it can be of the same size; Infinity is larger than all of the natural numbers. There is a smallest infinite number, "countable infinity". It is the counting number for all of the whole numbers. It is also the counting number of the rational numbers. The mathematical notation is the Hebrew letter aleph with a subscript zero; formula_2. It is spoken "aleph naught".
It was a surprise to learn that there are larger infinite numbers. The number of real numbers, that is, all numbers with decimals, is larger than the number of rational numbers, the number of fractions. This shows that there are real numbers which are not fractions. The smallest infinite number greater than formula_2 is formula_4 (aleph one). The number of mathematical functions is the next infinite cardinal number, formula_5.
And these numbers, called aleph numbers, go on without end.
A different "type" of infinity are the ordinal numbers, beginning "first, second, third, ...". The order "first, second, third, ..." and so on to infinity is "different" from the order "ending" "..., third, second, first". The difference is important for mathematical induction. The simple "first, second, third, ... " has the mathematical name: the Greek letter omega with subscript zero: formula_6. (Or simply omega formula_7.) The infinite series ending "... third, second, first" is formula_8.
The third "type" of infinity has the symbol formula_1. This is treated as addition to the real numbers or the complex numbers. It is the result of division by zero, or to indicate that a series is increasing (or decreasing) without bound. The series 1, 2, 3, ... increases without upper bound. This is written: the limit is formula_10. In calculus, the integral over all real numbers is written: formula_11
Each kind of infinity has different rules.
formula_12 Addition with "alephs" is commutative.
formula_13 Multiplication with "alephs" is commutative.
formula_14
formula_15.
formula_16. Addition with "omegas" is not commutative.
formula_17. Multiplication with "omegas" is not commutative.
formula_18
formula_19
formula_20
formula_21 Otherwise, division by infinity is not meaningful. Subtraction with infinity is not meaningful.
January
January (Jan.) is the first month of the year in the Julian and Gregorian calendars, coming between December (of the previous year) and February (of the current year). It has 31 days.
January begins on the same day of the week as October in common years, and April and July in leap years. January ends on the same day of the week as February and October in common years, and July in leap years.
January is named for Janus, the Roman god of doors and gates.
January and February were put on the calendar after all the other months. This is because in the original Roman calendar, winter did not have months. Although March was originally the first month, January became the new first month because that was when people chose the new consuls (Roman leaders). The month has 31 days.
January is a winter month in the Northern Hemisphere and a summer month in the Southern Hemisphere. In each hemisphere, it is the seasonal equivalent of July in the other. Perihelion, the point in its orbit where the Earth is closest to the Sun, also occurs in this month, between January 2 and January 5. January begins on the same day of the week as October in common years and on the same day of the week as April and July in leap years. January ends on the same day of the week as February and October in common years and on the same day of the week as July in leap years. January is the only month of the year that always has a "twin" - a month that both begins and ends on the same day of the week as it does. In a common year, this is October, and in a leap year, July.
Every year, January both starts and finishes on the same day of the week as May of the previous year, as each other's first and last days are exactly 35 weeks (245 days) apart.
In common years immediately before other common years, January starts on the same day of the week as April and July of the following year, and in leap years and years immediately before that, September and December of the following year. In common years immediately before other common years, January finishes on the same day of the week as July of the following year, and in leap years and years immediately before that, April and December of the following year.
January's flower is the carnation with its birthstone being the garnet. The meaning of the garnet is constancy.
The first day of January is called New Year's Day. It is said that it became this date when Roman consuls took office on this day in 153 BC. Different calendars across Europe made this the start of the New Year at different times, as some observed it on March 25.