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

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In this video, we go over a topic that many people graze over but don't really conquer. What in the world is a Natural Number? What's a Whole Number? We say Integers all the time, but how do they really differ from Rational numbers? And what in the world is an Irrational Number?
We find out in the end that these number classifications sometimes wrap around each other (as larger classifications of numbers altogether). Let's learn about all the different types of classifications of numbers for the Real Numbers!

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You should pay attention on some question traps: √9 looks like Irrational. actually is not because √9 = 3 . So its a rational. π/π also looks like Irrational. in fact π/π = 1 so its a rational too.

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Natural Numbers - 0:31 | N | Only positive whole numbers. 1,2,3,4,5 - Does not include 0 nor decimals. Whole Numbers - 1:15 | W | Natural Numbers + 0. 0,1,2,3. Integers - 2:46 | Z | Whole numbers + Negative numbers. No decimals or fractions. -2,-1,0,1,2. Rational Numbers - 3:22 | Q | Whole numbers, negative, positive numbers fractions and decimals. For fractions both must be integers to belong to rational numbers. 9 over 2, -2.6, 1 over 2, 3.3, 4. Irrational Numbers - 6:04 | P | Unlike any of the above numbers. Constant decimals. Pie = 3.141… Square root of 2 = 2.718… Great video!

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3:37 Why are the terms "p" and "q" - specifically - used to denote the two integers?

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Not too sure how it is that so many people ended up using p and q, but you can easily use 'a' and 'b' instead.. or for that matter any two letters for the variables! In the same way y = mx + b (the m is the slope but you could technically use a different letter, like 'g' for 'm' and 'u' for 'b'. But somehow we all ended up using the same letters over time!)

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Also what are the symbols for Irrational, Prime, and composite numbers?

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Irrational numbers are also frequently noted as R-Q

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Why is not π considered as rational as π =22/7 i.e of form p/q integer /integer?

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22/7 does not really equal to pi. It is an approximation of pi used in some applications. You are correct in considering that 22/7 must be a rational number-it is.

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