Seite - 46 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python 3.6, Band Second Edition

46 2 AFewMoreSteps at thepreviouscalculation inmoredetail.Letus repeat thecalculation,but this time printmoredecimals, In [1]: x = 4 In [2]: y = 1.0/(x+1) In [3]: print(’The value of y is: {:.17f}’.format(y)) The value of y is: 0.20000000000000001 So, what should have been exactly 0.2, is really a slightly different value! The inexact number representation gave us a small error. Usually, such errors are so small compared to the other numbers of the calculation, that we do not need to botherwiththem.Still,keepit inmind,sinceyouwillencounterthisissuefromtime to time. More details regardingnumber representationson a computer are given in Sect.6.6.3. 2.2.10 BooleanExpressions In programming, we often need to check whether something is true or not true, and then take action accordingly. This is handled by use of logical or boolean expressions, which evaluate to the Boolean values true or false (i.e., not true).7 In Python, these values are writtenTrue andFalse, respectively (note capital letters TandF!). The following session presents some examples of boolean expressions, while alsoexplaining theoperators involved: In [1]: x = 4 In [2]: # The following is a series of boolean expressions: In [3]: x > 5 # x greater than 5 Out[3]: False In [4]: x >= 5 # x greater than, or equal to, 5 Out[4]: False In [5]: x < 5 # x smaller than 5 Out[5]: True In [6]: x <= 5 # x smaller than, or equal to, 5 Out[6]: True In [7]: x == 4 # x equal to 4 Out[7]: True In [8]: x != 4 # x not equal to 4 Out[8]: False Boolean values may also be combined into longer expressions by use of and and or. Furthermore, preceding a boolean expression by not, will effectively switch 7 https://en.wikipedia.org/wiki/Boolean_data_type.