praharmitra said:they are quite different. Statement 1, is an assumption (which we are assuming to be true), whereas statement 2 is a...well its a statement (that may be true/false)
Also, consider the second statement
It says sqrt(n) is either integer or irrational. This means sqrt(n) could be sqrt(2/3) which is also irrational. However, it is not equivalent to saying n is an "integer" and not a perfect square..
praharmitra said:edit: ok, Statement 2 also says n>=1(missed that) so just do the entire same argument for sqrt(3/2), that'll also hold
dperkin2 said:No he still means they are not equivalent. Just plug in 3/2 instead of 2/3 in his previous argument of why they are not equivalent.
The equivalence problem is a fundamental concept in mathematics and computer science that involves determining whether two objects or systems are equivalent or equal in some way.
The equivalence problem is concerned with determining whether two objects are equivalent in some way, while the equality problem is concerned with determining whether two objects are exactly the same in every aspect.
Some examples of the equivalence problem include determining whether two mathematical expressions are equivalent, whether two physical systems have the same properties, or whether two programming languages have the same functionality.
There are several methods for solving the equivalence problem, including using logical or mathematical proofs, conducting experiments or tests, or using algorithms or heuristics to compare and analyze the objects or systems in question.
The equivalence problem is important in science and technology because it allows us to determine whether different objects or systems are equivalent, which can help us to understand and solve complex problems, identify patterns, and make predictions. It is also crucial in fields such as cryptography, where determining the equivalence of different encryption methods is essential for ensuring security.