How many means what in math

Thus, if A and B are the two sets of colors above, then we have,. The intersection of two sets is the set containing only elements that are in both. For example, the intersection of A and C would be denoted as follows:. We will begin where every child begins—with counting. Notice the set notation. This is critical, and provides us with an important characterization:. Thus, the counting numbers—one, two, seventy-three, a million, and so on—are elements of the set of natural numbers.

The set of natural numbers has some properties that should be noted. First, of course, is that this set is ordered. This may seem so obvious as to be beneath our notice, but we will find as we start to really learn mathematics as opposed to just memorizing procedures that such niceties can sometimes take on surprising significance.

In fact we can do better with the natural numbers than saying merely that they are ordered. They have a property that we call being well-ordered:. Notice that there is not always a largest element; the set of all even numbers, the set of all multiples of 5, and the set of all the natural numbers greater than 37 are examples of sets that have no greatest element.

This business of not having a largest element is something every child notices at some point and then experiences her or his first brush with the idea of infinity.

We know that there isn't a largest natural number because, intuitively at least, we know the following principle which is sometimes called the Archimedian principle :. Another way of saying this is that the natural numbers are closed under addition. That is, take any two natural numbers and add them, and you get another natural number.

Addition can't take you outside of the set. Notice that the natural numbers are also closed under multiplication which makes sense, since multiplication is just repeated addition. The natural numbers are the only numbers we need for one of the most imporant results in classical mathematics, which comes down to us from antiquity it is found in Euclid's Elements.

This result is called the Fundamental Theorem of Arithmetic , which every numerate person should know. Students often ask why zero isn't included in the set of natural numbers. Well, sometimes it is. Many texts describe a set called the whole numbers , by which is meant the natural numbers with zero included. This terminology isn't used much, however, and mathematicians will usually make clear whether they intend to include zero when discussing or using the natural numbers.

It is well to separate zero conceptually from the natural numbers because it is really a very different kind of thing. Its historical development is quite different, too. People were counting for millenia before zero was ever thought of. In fact its first use is thought to have been in India in the 6th or 7th century, and came to us—like so much of the mathematics that we use in the western world—by way of Arabic culture in about the 11th century. It's notable that native Americans, specifically the Mayan civilization, also developed a concept of zero independently of the old world.

So anyway, while zero is optional in the natural numbers, it is always found in our next set…. We said that the set of natural numbers is closed under addition and multiplication, but of course there are other operations with numbers. Subtraction, for instance. If we take away two from three, then there is no problem because the remainder is one, and one is in the set of natural numbers.

What happens, however, if we want to go the other way and take three from two? We get a negative number, and negative numbers aren't included in the set of natural numbers. In order to talk about negative numbers, we will need to introduce a new set:. This is the set of integers , and is always denoted by a bold faced Z.

This means the natural numbers are a subset of the integers, i. Historically, negative numbers didn't come into wide use until the late middle ages, circa the 14th century. After all, when did you last see a negative quantity? However, negative numbers can be very handy for calculations involving debt, and the Italians who invented banks were the first to recognize their importance in finance and to use them for that purpose. The integers are closed under addition, subtraction, and multiplication, but what about division?

The process of "choosing the operation" involves deciding which mathematical operation addition , subtraction , multiplication , or division or combination of operations will be useful in solving a word problem.

Probability of Two Events Occurring Together: Independent Just multiply the probability of the first event by the second. Order of operations tells you to perform multiplication and division first , working from left to right, before doing addition and subtraction.

Continue to perform multiplication and division from left to right. Addition Rule 2: When two events, A and B, are non-mutually exclusive, there is some overlap between these events. The probability that A or B will occur is the sum of the probability of each event, minus the probability of the overlap. Or Probability. In probability , there's a very important distinction between the words and and or.

And means that the outcome has to satisfy both conditions at the same time. Or means that the outcome has to satisfy one condition, or the other condition, or both at the same time. How many more meaning in math? Category: science space and astronomy. What does OFC mean? Of Course. What is a term in algebra? What is the addition? What is Mathematics in simple words? What does 4 mean in math?

In most English speaking countries the , does not have any mathematical function, it is simply used to make numbers easier to read. In some other countries, especially in Europe, the comma may be used instead of a decimal point and indeed, a decimal point may be used in place of a comma as a visual separator. This is explained in more detail on our Introduction to Numbers page. It occurs frequently in mathematics and is a mathematical constant. Pi is a circle's circumference divided by its diameter and has the value 3.

It is an irrational number, which means that its decimal places continue to infinity. However large a number you have, you can always have a larger one, because you can always add one to it. Infinity is not a number, but the idea of numbers going on for ever. You cannot add one to infinity, any more than you can add one to a person, or to love or hate. Pipe ' ' is also also referred to as vertical bar, vbar, pike and has many uses in mathematics, physics and computing. When an object or point moves in a cyclic pattern, or is subject to vibration or oscillation e.

See an introduction to geometry for more. The line connecting the centre of a regular polygon with one of its sides. The line is perpendicular at a right angle to the side. Geometric area is defined as the space occupied by a flat shape or the surface of an object. Area is measured in square units, such as square metres m 2.

For more, see our page on area, surface area and volume. An asymptote is a straight line or axis that is specifically related to a curved line.

As the curved line extends tends to infinity, it approaches, but never touches, its asymptote that is, the distance between the curve and the asymptote tends to zero. It occurs in geometry and trigonometry. A line of reference about which an object, point or line is drawn, rotated or measured.

In a symmetrical shape, an axis is usually a line of symmetry. A coefficient is a number or quantity multiplying another quantity. It is usually placed before a variable. In the expression 6 x , 6 is the coefficient and x is the variable.

The circumference is the length of the distance around the edge of a circle. It is a type of perimeter that is unique to circular shapes. For more, see our page on curved shapes. Data are a collection of values, information or characteristics, which are often numerical in nature.

They may be collected by scientific experiment or other observational means. They may be quantitative or qualitative variables. A datum is a single value of a single variable. See our page on Types of Data for more. Diameter is a term used in geometry to define a straight line that passes through the centre of a circle or sphere, touching the circumference or surface at both ends.

The diameter is twice the radius.