Styjun

While looking for infinity value, I found out that:
In case of Python 3.7, INFINITY > INFINITY - 1 returns False and returns same if we do INFINITY < INFINITY - 1.

In case of C++ also, I get the same result that is False.

Is this happening because we don't have a proper definition for INFINITY? Right now we just know that it's just a huge number and we can not say that INFINITY starts after some specific number 'X'.

Coming back to the problem:
Now, some number x is obviously greater than x-1. Why this is not case with INFINITY?

Python Code:

A = float('inf')
B = float('inf')

print(A > B-1) # returns False
print(A < B-1) # returns False

C++ Code:

#include <iostream>
#include <limits>
using namespace std;

int main() 
 double a = numeric_limits<double>::infinity();
 double b = numeric_limits<double>::infinity();

 if (a>(b-1))cout<<"TRUE";
 else cout<<"FALSE"<<endl; //returns else part- FALSE

 if (a<(b-1))cout<<"TRUE";
 else cout<<"FALSE"; //returns else part- FALSE

 return 0;

For any other number = 10, number > number - 1 will return True and number < number - 1 will return False.

Thinking arithmetically the assertion is correct that x < x - 1. However, that is not how computers "think". Floating point numbers suffer from limited precision. Not even this holds:

print(1e90 < 1e90 - 1) # False
print(1e90 == 1e90 - 1) # True

That is because 1e90 - 1 is rounded to 1e90 when using double precision.

Something similar happens when working with infinity values. Before comparing, the expression inf - 1 is evaluated.
What does - inf - 1 evaluate to? There is only a single value to represent positive infinity so inf - 1 evaluates to inf.

In consequence, when you compare inf < inf - 1 you actually compare inf < inf and that's why you get False.

Infinity is not a number, not at least a real/complex one. It cannot be represented as a single value in mathematical domains. As such, it's not a meaningful operation to perform arithmetic on an "infinity" or compare it with anything.

But the brave engineers over at IEEE did standardize one way of representing infinity in their floating point standards. Their vision of an "infinity" should be well specified in IEEE-754.