4 Boolean Variables and Conditional Execution

4.1 Boolean Variables

We have learned about three types of variables in Python: ints, floats, and strings. Another variable type is a boolean, which can be one of two values: True or False. You can assign a boolean variable in the same way that you assign numbers or string, using =

myBool = True

True must be capitalized so don’t try true or it won’t be a boolean

myBool = true

4.1.1 Boolean Logic

Often you will want to check to see if some condition is true. For example, maybe you want to know if the radius of a certain satellite’s orbit is bigger or smaller than Mercury’s orbit. To perform this check, there are several boolean operators that will return True or False. Take note of the boolean operators shown in the cell below along with the comments added to explain what they do.

r1 = 3.5e8
r2 = 2.7e6

r1 > r2 # Is r1 greater than r2
r1 < r2 # Is r1 less than r2
r1 >= r2 # Is r1 greater than or equal to r2
r1 <= r2 # Is r1 less than or equal to r2
r1 != r2 # Is r1 not equal to r2
r1 == r2 # Is r1 equal to r2

False

A word of caution about comparing Python floats using == is in order here. Python floats are stored as a 53-digit, base-2 binary number(that’s a mouthful). If you’re interested in what that means, we can talk more. If you’re not that interested, just know that when you define a float in Python, the number that is stored in the computer is not exactly the number that you think it is. This can cause problems when you are comparing two numbers that you think should be equal but actually aren’t equal in the computer.¹ The code below illustrates this problem.

a = 0.1
b = 3 * a
c = 0.3
print(b==c)  # Are they the same number?  You would think they would
             # be right?
print(" {:.5f} ".format(b))     # They sure look the same.
print(" {:.5f} ".format(c))     # They sure look the same.
print(" {:.45f} ".format(b))  #b--- out to 45 decimal places
print(" {:.45f} ".format(c))  #c--- out to 45 decimal places

False
 0.30000 
 0.30000 
 0.300000000000000044408920985006261616945266724 
 0.299999999999999988897769753748434595763683319

The first two print statements display the value of b and c to five decimal places. The second two print statements force Python to display the value of b and c out to 45 decimal places. Notice that the true value of b is not exactly equal to 0.3. This is why the statement print(b==c) returns False. The take home message here is that comparing two floats to see if they are equal is always a bad idea. A better way to check to see if two floats are equal (or close enough that we can say they are equal) is to check if the absolute value of their difference is very small, like this:

a = 0.1
b = 3 * a
c = 0.3
print(abs(b - c) < 1e-10)

True

4.1.2 Compound Comparisons (Logical Operators)

Comparisons like those shown above can be chained together to make compound comparisons using the and, or, and not operators.

Operator	Description
and	Tests for both being `True`
or	Tests for either being `True`
not	Tests for `False`

The and operator requires both inputs to be True in order to return True while the or operator requires only one input to be True in order to evaluate at True. The not operator is different in that it only takes a single input value and returns True if and only if the input is False. It is a test for False.

Truth tables are a good way to visualize the output from compound comparisons.

p	q	p and q	p or q
`True`	`True`	`True`	`True`
`True`	`False`	`False`	`True`
`False`	`True`	`False`	`True`
`False`	`False`	`False`	`False`

As a simple example, suppose you know the density (\(\rho\)) and speed of light (c) for two materials and you’d like to know if both values are bigger for material 1 or material 2.

To Do:

Predict the output for each compound comparison given below. Add your guess as a comment.

Now add appropriately-placed print statements to check your guesses.

Modify your guess as needed and discuss any questions with a neighbor.

c1 = 2.5e8
c2 = 2.48e8
ρ1 = 450
ρ2 = 580

c1 > c2 and ρ1 > ρ2
c1 < c2 and ρ1 < ρ2
c1 > c2 and ρ1 < ρ2
c1 < c2 and ρ1 > ρ2

c1 > c2 and not ρ1 > ρ2
c1 < c2 and not ρ1 < ρ2

c1 > c2 or ρ1 > ρ2
c1 < c2 or ρ1 < ρ2

True

4.1.3 Tests for Inclusion

You can check for inclusion using the Python in operator. This provides an easy way to see if a character (or word) is present in a long string. Let’s say you have a long string that contains the names of Jupyter’s moons (there are 79 of them!!) and you want to see if a certain moon is included in the list. The in statement let’s us quickly test to see if it is in the list. (see example below)

jupytermoons = "Metis,Adrastea,Amalthea,Thebe,Io,Europa,Ganymede,Callisto,Themisto,Leda,Himalia,Lysithea,Elara,Dia,Carpo,Euporie,Thelxinoe,Euanthe,Helike,Orthosie,Iocaste,Praxidike,Harpalyke,Mneme,Hermippe,Thyone,Ananke,Herse,Aitne,Kale,Taygete,Chaldene,Erinome,Aoede,Kallichore,Kalyke,Carme,Callirrhoe,Eurydome,Pasithee,Kore,Cyllene,Eukelade,Pasiphae,Hegemone,Arche,Isonoe,Sinope,Sponde,Autonoe,Megaclite"

"Cyllene" in jupytermoons

True

4.2 Conditions

Conditions allow the user to specify if and when certain lines or blocks of code are executed. Specifically, when a condition is true, the block of indented code directly below it will run.

4.2.1 `if` statement

The if statement is used to control when a block of code runs. Its usage is shown below ending in a colon and the block of code below indented with four spaces. Using the Tab key will also produce four spaces.

jupytermoons = "Metis,Adrastea,Amalthea,Thebe,Io,Europa,Ganymede,Callisto,Themisto,Leda,Himalia,Lysithea,Elara,Dia,Carpo,Euporie,Thelxinoe,Euanthe,Helike,Orthosie,Iocaste,Praxidike,Harpalyke,Mneme,Hermippe,Thyone,Ananke,Herse,Aitne,Kale,Taygete,Chaldene,Erinome,Aoede,Kallichore,Kalyke,Carme,Callirrhoe,Eurydome,Pasithee,Kore,Cyllene,Eukelade,Pasiphae,Hegemone,Arche,Isonoe,Sinope,Sponde,Autonoe,Megaclite"

if "Cyllene" in jupytermoons:
    found = True
    print("Found Cyllene in the list")
    
if "Matis" in jupytermoons:
    found = True
    print("Found Matis in the list")

Found Cyllene in the list

If the boolean statement after if is true, the indented code below it will run. If the statement is false, Python just skips the indented lines below. The end of an if code block is determined by the indentation; to signal the end of the block, simply step back the indentation.

4.2.2 `else` Statement

Sometimes there will be an alternate block of code that you want to run if the if statement evaluates to False. The else statement is used to specify this block of code, as shown below.

jupytermoons = "Metis,Adrastea,Amalthea,Thebe,Io,Europa,Ganymede,Callisto,Themisto,Leda,Himalia,Lysithea,Elara,Dia,Carpo,Euporie,Thelxinoe,Euanthe,Helike,Orthosie,Iocaste,Praxidike,Harpalyke,Mneme,Hermippe,Thyone,Ananke,Herse,Aitne,Kale,Taygete,Chaldene,Erinome,Aoede,Kallichore,Kalyke,Carme,Callirrhoe,Eurydome,Pasithee,Kore,Cyllene,Eukelade,Pasiphae,Hegemone,Arche,Isonoe,Sinope,Sponde,Autonoe,Megaclite"

if "Cyllene" in jupytermoons:
    found = True
    print("Found Cyllene in the string")
else:
    found = False
    print("Did not find Cyllene in the string")

    
if "Matis" in jupytermoons:
    found = True
    print("Found Matis in the string")
else:
    found = False
    print("Did not find Matis in the string")

Found Cyllene in the string
Did not find Matis in the string

Notice that the else statement must be followed by a colon and the block of code to be executed is indented, just as in the if block.

There is an additional statement called the elif statement, short for “else if”, which is used to add extra conditions below the initial if statement. The block of code below the elif statement only runs if the if statement is false and the elif statement is true. An example is given below.

jupytermoons = "Metis,Adrastea,Amalthea,Thebe,Io,Europa,Ganymede,Callisto,Themisto,Leda,Himalia,Lysithea,Elara,Dia,Carpo,Euporie,Thelxinoe,Euanthe,Helike,Orthosie,Iocaste,Praxidike,Harpalyke,Mneme,Hermippe,Thyone,Ananke,Herse,Aitne,Kale,Taygete,Chaldene,Erinome,Aoede,Kallichore,Kalyke,Carme,Callirrhoe,Eurydome,Pasithee,Kore,Cyllene,Eukelade,Pasiphae,Hegemone,Arche,Isonoe,Sinope,Sponde,Autonoe,Megaclite"

if "Matis" in jupytermoons:
    foundMatis = True
    print("Found Matis in the string")
elif "Cyllene" in jupytermoons:
    foundCyllene = True
    print("Found Cyllene in the string.")
else:
    foundCyl = False
    foundMatis = False
    print("Did not find Cyllene or Matis in the string")

Found Cyllene in the string.

It is worth noting that else statements are not required. If you leave the else statement off and the if statement is false, no code block will execute.

There is a library called Decimal that will fix a lot of these problems.↩︎