Classification of Numbers (Natural, Whole, Integers, Rational, Irrational, Real) - Nerdstudy

in this lesson we're going to be learning about the different classification of numbers which include natural numbers whole numbers integers rational numbers irrational numbers and real numbers so the most basic type of classification of numbers are the natural number and this is a symbol that we use to represent them natural numbers include numbers such as 1 2 3 4 5 and so on they are often referred to as counting numbers now natural numbers do not include 0 or any negative numbers as well as any decimals so an easy way to remember this is to think of it like this we all naturally count things starting from 1 and go on to 2 3 4 5 6 and so forth but rarely do we count starting from zero therefore this is the inner most basic classification of numbers the next layer of numbers are the whole numbers whole numbers can often be denoted using this symbol now the classification of whole numbers are exactly like natural numbers in that it includes all of the natural numbers and it also includes 0 so instead of starting from 1 whole numbers start from 0 another cool way to remember this is to think about it like this whole numbers are exactly the same as natural numbers except that they start with the number that looks like a whole therefore whole numbers include natural numbers and this means that any natural number is also considered a whole number but not necessarily the other way around since 0 is not a natural number do note however that the classification of these two are still a little bit hazy as some places might teach you that Nat Chua members do in fact include zero disregarding the classification of whole numbers entirely it is common to see that in set theory or in computer science since in these fields they actually do count starting from zero but for the sake of this video we're just going to include the classification of whole numbers as well the next classification of numbers is something you are likely to have heard of before they're called integers integers can often be denoted using this symbol integers include all the same numbers as whole numbers like 0 1 2 3 etc except they also include all the negatives of them as well such as negative 1 negative 2 negative 3 negative 4 and so on but again integers do not include decimals or fractions of numbers the next classification of numbers are called rational numbers which can be denoted using this symbol and again rational numbers encompass all of the other classification that we've mentioned so far as well as decimals and fractions however the decimal numbers must be numbers that can be expressed as a fraction where P and Q are integers and Q is not 0 so for example 17 over 3 is equal to 5 point 6 6 6 repeating and since the numerator and denominator are both integers this is in fact considered a rational number now whereas this looks fairly organized with its repeating sixes even something like 19 over 17 which yields this rather unpredictable looking decimal would still be considered a rational number and why because this is an integer and this is also an integer that is not the to zero okay so far so good so if I told you that I'm thinking of a number and that it is a natural number can you assume that this number is also a rational number well definitely you can also assume that it's a whole number since that's a bigger set you can even assume that it's also an integer since it's an even bigger set than that of a whole number and finally as we mentioned you can also assume that it's a rational number since rational numbers are a bigger set than the set of integers we can compare it to something like this if I said that there is a person in Tokyo can we also assume that this person is in Japan well obviously as well would we be correct to assume that this person is also in Asia absolutely since Tokyo is in Japan and because Japan is in Asia and finally would it be okay to assume that this person is on earth well of course because Earth is even bigger of a set than Asia good now there's a whole different set of numbers that is not within any of these this set of numbers cannot be expressed as a fraction another way to describe this is that this set is completely separate from the rational numbers altogether fittingly so we can call these numbers irrational numbers an example of an irrational number would be pleye and we know that pi is a never-ending number that does not repeat with a constant decimal or in a pattern fashion and this is what makes it irrational the square root of two also turns out to be an irrational number since it cannot be expressed as a fraction and lastly the definition of real numbers is last classification that we'll talk about although there are some other classifications that you might learn later on down the road real numbers are simply all of the rational and irrational numbers combined so pay close attention to how certain number sets are literally in the other sense but just remember that even though saying that a person in Tokyo must also be in Japan is correct the reverse isn't always correct if this person is in Japan it doesn't necessarily mean that they are in Tokyo maybe they're in Osaka or wherever else in Japan similarly while we can say for example that all national numbers are also integers we cannot say that all integers are natural numbers the same applies to the rest of the layers of classifications that we've learned so the classification of numbers might seem random but they will be used over and over again so it'll be well worth your time to learn it thoroughly right away and well that's it for this video guys and we hope to see you in the next one

Channel: Nerdstudy

Views: 547,651

Rating: 4.8511596 out of 5

Keywords: Classification of Numbers, Natural Number, Whole Numbers, Integers, Rational Numbers, Irrational Numbers, Real Numbers

Id: vbPUS-0Wbv4

Length: 7min 58sec (478 seconds)

Published: Sat Feb 11 2017