Examples of real values in the following topics:
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- There is no such value such that when squared it results in a negative value; we therefore classify roots of negative numbers as "imaginary."
- What does it mean, then, if the value under the radical is negative, such as in $\displaystyle \sqrt{-1}$?
- There is no real value such that when multiplied by itself it results in a negative value.
- This means that there is no real value of $x$ that would make $x^2 =-1$ a true statement.
- When the radicand (the value under the radical sign) is negative, the root of that value is said to be an imaginary number.
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- Real GDP growth is the value of all goods produced in a given year; nominal GDP is value of all the goods taking price changes into account.
- The real GDP is the total value of all of the final goods and services that an economy produces during a given year, accounting for inflation .
- In economics, real value is not influenced by changes in price, it is only impacted by changes in quantity.
- Real values measure the purchasing power net of any price changes over time.
- Real GDP accounts for inflation and deflation.
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- When we talk about American values, we often have in mind a set of ideal values.
- Along with every value system comes exceptions to those values.
- With these exceptions, real values emerge.
- Whereas we might refer to ideal values when listing American values (or even our own values), the values that we uphold in daily life tend to be real values.
- In ideal culture, marriage is forever, but in real culture, many marriages end in divorce.
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- Absolute value can be thought of as the distance of a real number from zero.
- In mathematics, the absolute value (sometimes called the modulus) of a real number $a$ is denoted $\left | a \right |$.
- For example, the absolute value of 5 is 5, and the absolute value of −5 is also 5, because both numbers are the same distance from 0.
- When applied to the difference between real numbers, the absolute value represents the distance between the numbers on a number line.
- Other names for absolute value include "numerical value," "modulus," and "magnitude."
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- The real option creates economic value by generating future decision rights for management.
- A key feature is that the real option creates economic value by generating future decision rights - specifically, by offering management the flexibility to act upon new information such that the upside economic potential is retained while the downside losses are contained .
- Another value-creating aspect of real options can be found in abandonment.
- Real investments are often made not only for immediate cash flows from the project, but also for the economic value derived from subsequent investment opportunities.
- Projects with real options can be evaluated using a range of possible profits.
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- In other words, two different values of $x$ can have the same $y$-value, but each $y$-value must be joined with a distinct $x$-value.
- Both graphs include all real numbers $x$ as input values, since both graphs continue to the left (negative values) and to the right (positive values) for $x$ (inputs).
- The curves continue to infinity in both directions; therefore, we say the domain for both graphs is the set of all real numbers, notated as: $\mathbb{R}$.
- The graph of $f(x)=x^2$ (red) has the same domain (input values) as the graph of $f(x)=-\frac{1}{12}x^3$ (blue) since all real numbers can be input values.
- The range of the blue graph is all real numbers, $\mathbb{R}$.
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- The real rate is the nominal rate minus inflation.
- In the case of a loan, it is this real interest that the lender receives as income.
- A lender would have no net benefit from such a loan because inflation fully diminishes the value of the loan's profit.
- Where r is the real rate, i is the inflation rate, and R is the nominal rate.
- The real rate can be described more formally by the Fisher equation, which states that the real interest rate is approximately the nominal interest rate minus the inflation rate: 1 + i = (1+r) (1+E(r)), where i = nominal interest rate; r = real interest rate; E(r) = expected inflation rate.
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- A root, or zero, of a polynomial function is a value that can be plugged into the function and yield $0$.
- The zero of a function, $f(x)$, refers to the value or values of $x$ that will result in the function equaling zero, $f(x)=0$.
- This section specifically deals with polynomials that have real coefficients.
- (An example of a non-real number would be $\sqrt -1$.)
- Even though all polynomials have roots, not all roots are real numbers.
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- Nominal GDP, or unadjusted GDP, is the market value of all final goods produced in a geographical region, usually a country.
- That market value depends on the quantities of goods and services produced and their respective prices.
- In other words, real GDP is nominal GDP adjusted for inflation.
- Real GDP reflects changes in real production.
- It is calculated by dividing nominal GDP by real GDP and multiplying by 100.
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- Elementary differential equations and boundary value problems.
- Real analysis.