OMG what does it mean when math talks about " REAL NUMBERS" Im so confused!?

Question

Ya heres the sad part im in high school and in my algebra book it always said something like, "Closure property: For all "REAL NUMBERS" a & b!" It uses the term real numbers constantly but i dont know what it is. Please help! Thanks!

someone said its a rational and irrational number. What are those?

Answer 1

"Real number" means "NOT pure imaginary or complex numbers."

So what are pure imaginary or complex numbers? They are numbers like:

(i) 5i, i/7, - πi, ... etc. (all pure imaginaries), or

(ii) 3 + 4i, (1 + √2i)/√3, sin 30 + i cos 30, e^(iπ/3 ), ... etc. (all of which are complex numbers).

These numbers all involve " i," the "square root of - 1," that is: x = i is the (pure imaginary) solution to the equation x^2 = - 1.

(Believe me, such numbers may be unfamiliar to you now, but they "exist," in fact it is hard to imagine [pun not intended] modern society developing without the use of such numbers in so many technological fields. I will grant you, however, that such "imaginary numbers" appear to have remarkable and unanticipated properties when one first encounters them. However, like anything else in algebra, one learns to handle them with confidence and effectiveness.)

Real numbers are those that you can imagine occupying a "real number line" from - ∞ to + ∞. (In some problems, however, you may be told to restrict your attention to real numbers within a certain range, say 0 < x < 5, for example.)

Real numbers can be:

(a) RATIONAL, which means expressible as a whole number fraction such as 355/113 (check that one out --- it's a pretty good approximation to π), OR:

(b) IRRATIONAL, which means they CAN'T be expressed as a whole number fraction.

Numbers like √2, e, π are all irrational numbers; such numbers can additionally be divided into "algebraic" (the solution to a finite, real algebraic equation like √2, the solution to x^2 = 2), and "transcendental" (NOT the solution to a finite, real algebraic equation). The previously mentioned e and π are examples of transcendental numbers.

Live long and prosper.

Answer 2

Real numbers are numbers whether as simple as 0, 1/2, 2.1, 99/100 or numbers with no end like Pi or Infinity. They exist normally.

They're called Real Number because there are also Imaginary numbers which are not Real. The Square root of -1 is one. You cannot express the answer as a number.

Answer 3

Closure, It means if you divide two numbers or get a square
root the answer is the same kind of number For instance you
can't have subtraction of any two counting numbers unless
you can have zero and negative numbers, hence integers and
subtraction is closed in integers, not counting numbers,
Similarly, you can't have division by any two integers unless
you have rational numbers, and you can't have square roots
of integers and rationals unless you let in irrational numbers,
and you can't have arctangents unless you have transcendental numbers like pi. the whole collection is the
real numbers

Answer 4

Real numbers are all numbers rational (4), irrational (pi), positive, negative, or zero. In opposition, imaginary numbers are numbers that cannot exist, but are often used to solve various problems. Imaginary numbers are nonreal numbers whose square is a negative real number. When we find the square root of a negative number, the solution is given in terms of "i".

Answer 5

Real numbers may be described informally as numbers that can be given by an infinite decimal representation. Real numbers include both rational and irrational numbers.

Answer 6

Real vampires if existed would not spend their time on a forum answering questions about their existence they would keep it secret anyone who says they are one are not. Its all a fantasy and makes you feel psychological better about yourself like you have more purpose in life and feel part of a family and its a dangerous fantasy if you want to drink blood or take energy from people then no good will come from it and which will only lead to a number of diseases as listed above. You have more potential to use your brain and make a good life for yourself if you try. Don't fall into this whole bad vampire fantasy get yourself a good education and healthy lifestyle and if want to role play as one do it but don't go any further..

Answer 7

Real Numbers are numbers without and i. So 1,2,3 and so on (regular numbers). An i is when you get a answer to a quadratic equation that is negative. If the answer is -3 you would put it a 3i. i stands for imaginary or complex numbers.

Answer 8

real numbers are basically any number you can think of at this point in your education, you probably have never even seen imaginary numbers

it helps to understand what an imaginary number is to explain your question

imaginary number = sqrt ( -1 )

since you cant find solution for sqrt of (-1) in most texts books sqrt(-1 is written as a bold i

any number not containing i is real

Answer 9

Real numbers are pretty much all numbers. I have no idea what imaginary numbers are...We haven't gotten to them yet in 8th grade algebra...

Answer 10

All rational and irrational numbers.