We can only guess, but this code

`abs(i - 0)`

is attempting to materialize a *distance* between `i`

and `0`

, like we would do

abs(x - y)

Note that it has a cost CPU-wise:

>>> 6 0 LOAD_GLOBAL 0(abs) 3 LOAD_GLOBAL 1(i) 6 LOAD_CONST 1(0) <= == not optimized out 9 BINARY_SUBTRACT <= == not optimized out 10 CALL_FUNCTION 1(1 positional, 0 keyword pair) 13 RETURN_VALUE

Division is done using the / operator. Notice that you don’t want to divide by zero, lest you run into a ZeroDivisionError.,In programming, you often want to find the remainder of a divide operation. This can be done with the modulus operator %.,Python also has an integer division operator //. This floors the quotient for you. In other words, it rounds down the result of the divide operation. Here are a few examples of standard division vs integer floored quotient division.,Subtraction is done with the – operator. Again we can subtract integer numbers, floating-point numbers, or a mix of the types.

Sorting numbers in Python usually happens when you have a list of numbers or some other type of collection of numbers like a tuple or a dictionary of numbers. Imagine we have these numbers stored in a list.

nums = [1, 3, 2, 5, 4]

One way we could sort these numbers in Python is by using the built-in **sorted()** function.

sorted(nums)

`sorted(nums)`

`[1, 2, 3, 4, 5]`

`sorted(nums, reverse=True)`

`[5, 4, 3, 2, 1]`

If we look at our ** nums** variable, the sort order is still how it was originally assigned. This shows that the sorted() function left the original list as is.

nums

Last Updated : 13 Jun, 2022

```
Input: 14
Output: 6
Steps:
14 - 1 = 13
13 - 1 = 12
12 - 1 = 11
11 - 1 = 10
10 - 1 = 9
9 - 9 = 0
Input: 20
Output: 12
Numbers after series of steps:
20, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 0
```

6

6

Return the complementary error function at x. The complementary error function is defined as 1.0 - erf(x). It is used for large values of x where a subtraction from one would cause a loss of significance.,Whether or not two values are considered close is determined according to given absolute and relative tolerances.,For some applications, it may be more convenient to have the least integer a such that n ≤ a², or in other words the ceiling of the exact square root of n. For positive n, this can be computed using a = 1 + isqrt(n - 1).,These functions cannot be used with complex numbers; use the functions of the same name from the cmath module if you require support for complex numbers. The distinction between functions which support complex numbers and those which don’t is made since most users do not want to learn quite as much mathematics as required to understand complex numbers. Receiving an exception instead of a complex result allows earlier detection of the unexpected complex number used as a parameter, so that the programmer can determine how and why it was generated in the first place.

```
>>> sum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1])
0.9999999999999999
>>>
fsum([.1, .1, .1, .1, .1, .1, .1, .1, .1, .1])
1.0
```

```
>>> from math
import exp, expm1
>>>
exp(1e-5) - 1 # gives result accurate to 11 places
1.0000050000069649e-05
>>>
expm1(1e-5) # result accurate to full precision
1.0000050000166668e-05
```

```
sqrt(sum((px - qx) ** 2.0
for px, qx in zip(p, q)))
```

```
def phi(x):
'Cumulative distribution function for the standard normal distribution'
return (1.0 + erf(x / sqrt(2.0))) / 2.0
```

```
>>>
import math
>>>
math.nan == math.nan
False
>>>
float('nan') == float('nan')
False
>>>
math.isnan(math.nan)
True
>>>
math.isnan(float('nan'))
True
```

23. Write a Python program that accept a positive number and subtract from this number the sum of its digits and so on. Continues this operation until the number is positive. Go to the editor Click me to see the sample solution,20. Write a Python program to find the number of zeros at the end of a factorial of a given positive number. Go to the editor Range of the number(n): (1 <= n <= 2*109). Click me to see the sample solution,7. Write a Python program to count the number of each character of a given text of a text file. Go to the editor Click me to see the sample solution,3. Write a Python program to remove and print every third number from a list of numbers until the list becomes empty. Click me to see the sample solution

**The Any() Function:**

```
>>> arrival_hours = {
'Mon': 8.5,
'Tue': 8.75,
'Wed': 9,
'Thu': 8.5,
'Fri': 8.5
} >>>
arrival_checks = [x > 8.75
for x in arrival_hours.values()
] >>>
any(arrival_checks)
True
```