diff --git a/source/frontmatter.ptx b/source/frontmatter.ptx index e5caa11..5866a9c 100644 --- a/source/frontmatter.ptx +++ b/source/frontmatter.ptx @@ -59,12 +59,6 @@
-- Simon King, University of Jena* -
-Vartuyi Manoyan, Wright College @@ -89,18 +83,6 @@
- Soma Dey, Wright College* -
-- Sydney Hart, Wright College* -
-
Ted Jankowski, Wright College
diff --git a/source/relations/ch-relations.ptx b/source/relations/ch-relations.ptx
index 9d50e30..1f331aa 100644
--- a/source/relations/ch-relations.ptx
+++ b/source/relations/ch-relations.ptx
@@ -16,4 +16,5 @@
+ Proofs are fundamental to mathematics and computer science, providing the means to demonstrate the truth of statements. One powerful proof technique is mathematical induction, which is especially useful for proving properties about integers, sequences, and recursive structures. Induction allows us to prove that a statement holds for all natural numbers by first proving it for a base case and then showing that if it holds for an arbitrary case, it must also hold for the next case.
+
+ A direct proof is a straightforward method of proving a statement by assuming the premises and logically deriving the conclusion. For example, let’s prove that the sum of two even integers is always even.
+
+ This simple example shows that the sum of two even numbers
+ Mathematical induction is a proof technique used to prove statements about natural numbers. It consists of two steps:
+
+
+
+ Together, these steps show that the statement holds for all natural numbers. Let’s use induction to prove that the sum of the first
+ In the base case, for
+ Strong induction is similar to regular induction, but in the inductive step, we assume the statement is true for all values up to some
+ Let’s prove that any integer greater than 1 can be written as a product of prime numbers using strong induction.
+
+ Using strong induction, we can show that any number
+
+