No, they are quite real. It is just that in some situations it makes sense to use negative numbers, in others not.
Temperature in cold areas are negative. Below sea level is negative altitude. Degrees left on the world coordinates.
It depends on the combination. Real numbers are closed with respect to arithmetical operations (+, -, *, /), as well as integer powers (exponents). So a combination of real numbers using any of these operators will yield a real number. But the set is not closed with respect to some fractional powers - for example, the square root of a negative number is not real.It depends on the combination. Real numbers are closed with respect to arithmetical operations (+, -, *, /), as well as integer powers (exponents). So a combination of real numbers using any of these operators will yield a real number. But the set is not closed with respect to some fractional powers - for example, the square root of a negative number is not real.It depends on the combination. Real numbers are closed with respect to arithmetical operations (+, -, *, /), as well as integer powers (exponents). So a combination of real numbers using any of these operators will yield a real number. But the set is not closed with respect to some fractional powers - for example, the square root of a negative number is not real.It depends on the combination. Real numbers are closed with respect to arithmetical operations (+, -, *, /), as well as integer powers (exponents). So a combination of real numbers using any of these operators will yield a real number. But the set is not closed with respect to some fractional powers - for example, the square root of a negative number is not real.
The set of real numbers is not closed under powers. That is to say, there are some equations of the form y = xa which do not have a solution within the set. Typical example: x is negative, a = 0.5
There are lots of subsets; some of the ones that are commonly used are: rational numbers; irrational numbers; positive numbers; negative numbers; non-negative numbers; integers; natural numbers. Remember that a subset simply means a set that is contained in another set. It may even be the same set. So the real numbers are a subset of themselves. The number {3} is a subset of the reals. All the examples above are subsets as well. The set {0,1, 2+i, 2-i} is NOT a subset of the real numbers. The real numbers are a subset of the complex numbers.
Of the "standard sets" -10 belongs to: ℤ⁻ (the negative integers) ℤ (the integers) ℚ⁻ (the negative rational numbers) ℚ (the rational numbers) ℝ⁻ (the negative real numbers) ℝ (the real numbers) ℂ (the complex numbers) (as ℤ ⊂ ℚ ⊂ ℝ ⊂ ℂ). Other sets are possible, eg the even numbers.
No, they are quite real. It is just that in some situations it makes sense to use negative numbers, in others not.
Temperature and Money Issues.
Temperature in cold areas are negative. Below sea level is negative altitude. Degrees left on the world coordinates.
Not necessarily. Negatives can be rational or irrational - each one is the same as its positive counterpart.
The set of real numbers is not closed under powers. That is to say, there are some equations of the form y = xa which do not have a solution within the set. Typical example: x is negative, a = 0.5
It depends on the combination. Real numbers are closed with respect to arithmetical operations (+, -, *, /), as well as integer powers (exponents). So a combination of real numbers using any of these operators will yield a real number. But the set is not closed with respect to some fractional powers - for example, the square root of a negative number is not real.It depends on the combination. Real numbers are closed with respect to arithmetical operations (+, -, *, /), as well as integer powers (exponents). So a combination of real numbers using any of these operators will yield a real number. But the set is not closed with respect to some fractional powers - for example, the square root of a negative number is not real.It depends on the combination. Real numbers are closed with respect to arithmetical operations (+, -, *, /), as well as integer powers (exponents). So a combination of real numbers using any of these operators will yield a real number. But the set is not closed with respect to some fractional powers - for example, the square root of a negative number is not real.It depends on the combination. Real numbers are closed with respect to arithmetical operations (+, -, *, /), as well as integer powers (exponents). So a combination of real numbers using any of these operators will yield a real number. But the set is not closed with respect to some fractional powers - for example, the square root of a negative number is not real.
There are lots of subsets; some of the ones that are commonly used are: rational numbers; irrational numbers; positive numbers; negative numbers; non-negative numbers; integers; natural numbers. Remember that a subset simply means a set that is contained in another set. It may even be the same set. So the real numbers are a subset of themselves. The number {3} is a subset of the reals. All the examples above are subsets as well. The set {0,1, 2+i, 2-i} is NOT a subset of the real numbers. The real numbers are a subset of the complex numbers.
There are lots of situations in the real world in which there are opposites, which can conveniently be expressed with positive/negative numbers. Here are some examples:Having money (positive), having a debt (negative)Getting a profit (positive) or a loss (negative) with a business ventureAn altitude above (positive) or below (negative) sea levelGaining points or losing points in a gameMoving in one direction or in the opposite direction. In this case, it is quite arbitrary which direction is chosen as positive.
Some people work as a teacher or a mathmetition, they use negative numbers in their everyday lives. Some people use negative numbers when they are overdue.
Integers are a subset of real numbers. All integers are real numbers, but not the other way around. Real numbers, without going into great detail, are numbers that can be drawn on a standard x-y graph. This includes integers, fractions & decimals, common constants such as pi and e, etc. Taking the square root of negative number would result in an imaginary number (which are not a real numbers.) Integers are essentially whole numbers (numbers that can be written without a decimal or in fraction form).
Please don't write "the following" if you don't provide a list. This is the situation for some common number sets:* Whole numbers / integers do NOT have this property. * Rational numbers DO have this property. * Real numbers DO have this property. * Complex numbers DO have this property. * The set of non-negative rational numbers, as well as the set of non-negative real numbers, DO have this property.