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# are negative numbers real numbers?

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Yes

real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2.4871773339.... The real numbers include both rational numbers, such as 42 and −23/129, and irrational numbers, such as π and the square root of 2, and can be represented as points along an infinitely long number line.

• Are Negative Numbers Real Numbers

• No. Addition and subtraction (a=b+c) & (a=b-c) work the same as the real world.

Multiplication and division do not. If you look at the number line, everything to the right of zero works as it does in the real world. Everything to the left (negative numbers) does not.

For example, (-2) (-2) = 4, which has the result leaping from the left side past zero to positive 4, but (-2) (-2) (-2) gives a logical, real world result of -8.

There should be symmetry. If (2) (2) = 4, then (-2) (-2) should equal -4. There is a fundamental problem with the concept of multiplication or the commutative property.

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Negative numbers are in fact real numbers, as is 0. Actually, you can use them as the base of exponential functions, but the functions then become very messy (to put it mildly), and require the use of complex numbers. If you haven't been exposed to complex numbers, the rest of my answer probably won't make much sense; sorry. Try a=-1. What is f(1/2)? Both (-i) and (i), when squared, give -1. So, f(1/2) = -i or i are both reasonable answers. f is a function, so it has to give a single output, so we have to pick one or the other. In polar form i has a smaller argument, so let's say we choose it and make f(1/2) = i. What is f(1/3)? There are actually three answers--two complex and one real--but let's pick the real one and say f(1/3) = -1. Now, what is f(1/pi)? It turns out there are infinitely many answers, though you can again pick a smallest answer reasonably. To define an exponential function a^x for a<0, you need to allow complex numbers as output, and you need to choose which root you want to use for each output. Even after all that work, your function is horribly discontinuous. It bounces between the complex plane and the real line and is generally pretty useless.

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• I hold the view (it is only mine as far as I know) that negative numbers are not real. They are the first form of imaginary number. You can not give someone an apple when there are no apples to be given. Owing someone an apple is a convention and debt is no more than an intellectual concept. If someone owed you an apple and a crippling disease killed off all apple trees you would would be hard pressed to repay the debt. The concept of debt requires the assumption the real commodity with which to service the debt can be available at some point. Reality does not always bear this out. Negative numbers are extremely useful, as are imaginary numbers for many engineering purposes. However, you have to be very wary of when reality will have its say irrespective of what the maths says.

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6 years ago

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• Anonymous
1 decade ago

I like to think of negative numbers as debts--I understand debts. So, if you had -5 dollars, you would owe 5 dollars to someone, and if you earned 10 bucks, you'd have to pay off the -5, and you'd end up with 5 dollars in your pocket.

• yes negitiv numbers are real but they are not whole number 0,1,2,3,4 are te whole numbers

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