Description
1. Floating-point numbers are a way to represent real numbers in computers using a
finite number of bits, expressed in scientific notation as a combination of a sign, a
significand, and an exponent. This format allows representation of a wide range of
values but introduces rounding errors and precision limits, leading to potential inaccuracies in arithmetic operations. As was stated in class, this space of numbers are not
associative.
Within your python terminal, demonstrate that floating point numbers are not associative using the following values: a = 1.0, b = 108
, c = −108
.
Note: Exponentials are written using “E”. For example, 103
can be written as 1E3.
2. The example given in class used {1, 2, 3} with a ◦ b = max{a, b} and a ∗ b = min{a, b}.
Demonstrate why 2 has no inverse under both operations (you can do this exhaustively).
3. Consider the space with {0, 1, 2} with operation a ◦ b = (a + b) mod 3. What axioms
are satisfied? (You can skip the distributive property since there is only one operation.)