What is the above supposed to be saying?amiv4 said:Homework Statement
Prove that Square = {x ∈ N|∃y : N. x = y^2} is an infinite set.
amiv4 said:Homework Equations
Definition 0.1. A set A is infinite if there is an injection f : A → A that is not also a surjection.
The Attempt at a Solution
I get how to show that there is an injection, but i don't get how to show that it is also not a surjection
An infinite set is a set that has an uncountable number of elements. This means that there is no limit to the number of elements in the set and it cannot be exhausted by counting.
In mathematics, a square is a geometric shape with four equal sides and four equal angles, forming a right angle at each corner. It is also known as a regular quadrilateral.
Yes, a square can be considered an infinite set. In terms of set theory, a square can be defined as an infinite set of points that are equidistant from a central point.
A square can be proved to be an infinite set by showing that it has an uncountable number of elements. This can be done by using the Cantor diagonal argument, which states that any attempt to count the elements of an infinite set will always result in a larger uncountable set.
Yes, there are other methods to prove that a square is an infinite set. One method is by using the concept of one-to-one correspondence, where each element in the set can be paired with a unique element in the set of natural numbers. Another method is by using the concept of limit in calculus, where the perimeter of a square can be shown to approach infinity as the length of its sides increases.