Final answer:
The smallest double precision number that satisfies '1+x!=1' in computer programming is called the machine epsilon, which is approximately 2.220446049250313e-16. This can be verified using code and confirmed by adding the epsilon value to 1 and checking if it is not equal to 1. Additionally, the equation '1+x/2=1' can be verified by substituting the epsilon value into the equation and checking if it holds true.
Step-by-step explanation:
Smallest Double Precision Number:
In computer programming, the smallest double precision number that satisfies '1+x!=1' is called the machine epsilon or epsilon. In most programming languages, it is denoted as 'eps' or 'DBL_EPSILON'. The value of epsilon for double precision is approximately 2.220446049250313e-16.
Verification with Code :
To verify that '1+x!=1', you can write code that adds epsilon to 1 and checks if the result is different from 1. Here's an example in Python:
x = 2.220446049250313e-16
if 1 + x != 1:
print('1 + x is not equal to 1')
This code will output '1 + x is not equal to 1', confirming the condition.
Verification of '1+x/2=1' :
To verify that '1+x/2=1', you can substitute the value of epsilon into the equation and check if it holds true. Here's the calculation:
x = 2.220446049250313e-16
result = 1 + x/2
if result == 1:
print('1 + x/2 is equal to 1')
This code will output '1 + x/2 is equal to 1', confirming the condition.