Set Notation and Venn Diagrams

It is an unintelligent machine with input and output collections.

The first three lowercase letters of the alphabet.

Input set

<p>Venn diagram</p> Signup and view all the answers

<p>Each input corresponds to exactly one output.</p> Signup and view all the answers

<p>Every element of the second set is matched with at least one element of the first set.</p> Signup and view all the answers

<p>Either by its description or by its rule.</p> Signup and view all the answers

<p>It is both one-to-one and onto.</p> Signup and view all the answers

<p>Every element of the first set is matched with only one element of the second set.</p> Signup and view all the answers

<p>An onto function is concerned with the range, while a one-to-one function is concerned with the domain.</p> Signup and view all the answers

<p>It is a polynomial function.</p> Signup and view all the answers

<p>A bijective function is a type of onto function.</p> Signup and view all the answers

<p>Domain</p> Signup and view all the answers

<p>f(x) = 2x</p> Signup and view all the answers

<p>Every element of the domain is matched with only one element of the range.</p> Signup and view all the answers

<p>To describe the process of a function</p> Signup and view all the answers

<p>f(x) = x^2</p> Signup and view all the answers

<p>Because it is difficult to list every input and output</p> Signup and view all the answers

<p>It is the ratio of two integers with no common multiple.</p> Signup and view all the answers

<p>f(n) = 2n - 1</p> Signup and view all the answers

<p>Uncountable</p> Signup and view all the answers

<p>f(n) = 2 - 1, if n is even, f(n) = n+1 - 2, if n is odd</p> Signup and view all the answers

<p>It maps the set of positive integers to the set of positive even numbers.</p> Signup and view all the answers

<p>A diagonal arrangement of infinite columns and rows.</p> Signup and view all the answers

<p>To prove that there are uncountably many real numbers in the interval [0, 1]</p> Signup and view all the answers

<p>Every real number in the interval [0, 1] can be written as a decimal, and the list shows a one-to-one correspondence between them</p> Signup and view all the answers

<p>It allows us to prove that there are uncountably many real numbers in the interval [0, 1]</p> Signup and view all the answers

<p>It provides a counterexample to the assumption</p> Signup and view all the answers

<p>They provide a one-to-one correspondence with the real numbers in the interval [0, 1]</p> Signup and view all the answers

<p>It proves that there are uncountably many real numbers in the interval [0, 1]</p> Signup and view all the answers

<p>That some infinities are larger than others</p> Signup and view all the answers

<p>Because b1 ̸= a11, b2 ̸= a22, and so on</p> Signup and view all the answers

<p>It highlights the difference between countable and uncountable infinite sets</p> Signup and view all the answers

<p>To illustrate the concept of different levels of infinity</p> Signup and view all the answers

<p>The list is incomplete and there are unlistable real numbers in [0, 1]</p> Signup and view all the answers

<p>It is an uncountably infinite set</p> Signup and view all the answers

<p>It proves that the set of real numbers in [0, 1] is countable</p> Signup and view all the answers

<p>That there are different levels of infinity</p> Signup and view all the answers

<p>It depends on the infinity of the size of new arriving passengers</p> Signup and view all the answers

<p>It is a countably infinite set</p> Signup and view all the answers