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Operators

Operators

Clearing Memory
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&   # and
|   # or
!   # not (negation)
Clearing Memory
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<−  # Left Assignment
=
<<−
->  # Right Assignment
->>
Clearing Memory
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<   Less than
>   Greater than
<=  Less than or equal to
>=  Greater than or equal to
==  Equal to
!=  Not equal to
Clearing Memory
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+   Addition
-   Subtraction
*   Multiplication
/   Division
^   Exponent
%%  Modulus(Remainder from division)
%/% Integer Division

Exercise: \(0^0\)

Clear the workspace, program \(0^0\) and verify your results:

Code
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rm(list=ls())        # Clear working space
cat("\f")            # Clear console
x = 0^0

While in mathematical analysis, the expression \(0^0\) is sometimes left undefined, in algebra and combinatorics, one typically defines \(0^0 = 1\). In computer sciences, the standard answer is \(0^0 = 1\).

Exercise: \(x!\)

Clear the workspace, program the factorial value \(100!\):

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rm(list=ls())        # Clear working space
cat("\f")            # Clear console
factorial(100)

Note that the mathematical symbol for factorial is given by \(x!\) whereas within the R language, ! operates as logical negation. The factorial is computed using the function factorial(100) and equal to 9.332622e+157.

Exercise: \(\pi\)

Clear the workspace, program the mathematical constant value \(\pi\):

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rm(list=ls())        # Clear working space
cat("\f")            # Clear console
pi

Note that the mathematical symbol for factorial is given by \(x!\) whereas within the R language, ! operates as logical negation. The factorial is computed using the function factorial(100) and equal to 9.332622e+157.

Exercise: Exponential \(e^x\), and logarithmic function \(\log(x)\), \(\ln(x)\)

Clear the workspace, program the following:

  • mathematical constant value \(e^1\),
  • compute \(\log(e)\).
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rm(list=ls())        # Clear working space
cat("\f")            # Clear console
exp(1)
log(exp(1))

R language provides a default logarithmic fuction log() operating as the natural logarithm. While there exists a short hand function log10(x) to carry out the base-10 as a special case, more general cases can be defined via inputting an extended argument: log(x, base = 10).

Exercise: Price of a three-year bond

Clear the workspace, program the following which reflect the present value of a three-year 3% annual coupon bearing bond with the face value of $100 and a 5% market discount rate:

\(\frac{5}{1+5\%} + \frac{5}{(1+5\%)^2} + \frac{5}{(1+5\%)^3} + \frac{100}{(1+5\%)^3}\)

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rm(list=ls())        # Clear working space
cat("\f")            # Clear console
exp(1)
3/(1+0.05) + 3/(1+0.05)^2 + 3/(1+0.05)^3 + 100/(1+0.05)^3

R language provides a default logarithmic fuction log() operating as the natural logarithm. While there exists a short hand function log10(x) to carry out the base-10 as a special case, more general cases can be defined via inputting an extended argument: log(x, base = 10).