commit 83109526c190873a4194ee10d6d0c20d7a6a4f0c
parent ad7f49e9f06427fab43486cb9c053eeb4b386682
Author: Andrew <andrewlaack1@gmail.com>
Date: Tue, 9 Apr 2024 22:12:17 -0500
Finished notes for the day. I will stick with standard wiki notes not vimwiki which is a bit more than I need/want.
Diffstat:
9 files changed, 27 insertions(+), 6 deletions(-)
diff --git a/CounterExample.md b/CounterExample.md
@@ -0,0 +1,7 @@
+# Proof By Counter Example
+
+Abstract Math Proof Technique
+
+## Notes
+
+**Definition:** Counter example proofs are similar to [[DirectProof.md]], but instead of assuming that they are true you assume they are false. From this assumption you then need to show that this is in some way fallacious.
diff --git a/DirectProof.md b/DirectProof.md
@@ -0,0 +1,7 @@
+# Direct Proof
+
+Abstract Math Proof Technique
+
+## Notes
+
+**Definition:** Direct proof is the assumption that the initial statement is true. You then show that it being true is true for all cases. These statements start with, "Let's assume x is true" we then continue on to prove what it is that x implies.
diff --git a/Induction.md b/Induction.md
@@ -1,4 +1,4 @@
-# Induction
+# Induction Proof
Proof by induction from W11 abstract algebra. Induction is used to prove a statement relating to infinite sets of elements. This is not to be confused with inductive reasoning which is assumptions based on past data.
@@ -28,4 +28,10 @@ When using induction the common form is $S_k \implies S_{k+1}$, but it is equall
When proving induction it is important to first state what the value of k+1 equates to. We then need to go from there to equate it to the other side of the statement. We should not assign the left and right together from the start because there would be nowhere to go from there instead do algebra to prove the statement is true.
-[[StrongInduction.md]] Is another type of induction.
+[[StrongInduction.md]] Is another type of induction.
+
+See also [[SmallestCounterExample.md]] for something similar to [[CounterExample.md]] of [[Induction.md]]
+
+It is important to note that a set must be [[WellOrdered.md]] for it to be possible to prove by induction.
+
+Another interesting thing that relates to induction is [[FibonacciNumbers.md]] in the sense that they are entirely reliant upon previous calculations to determine the next value in the set.
diff --git a/Math310.md b/Math310.md
@@ -4,4 +4,4 @@ This is the index for my main Math 310 notes.
# Main Links
-[[Induction]]
+[[Induction.md]]
diff --git a/MeshFilter.md b/MeshFilter.md
@@ -1,6 +1,6 @@
# Mesh Filter
-Unity game engine component [[Unity.md]]
+[[Unity]] game engine component
## Notes
diff --git a/MeshRenderer.md b/MeshRenderer.md
@@ -1,6 +1,6 @@
# Mesh Renderer
-Unity component [[Unity.md]]
+[[Unity]] Component
## Notes
diff --git a/StrongInduction.md b/StrongInduction.md
@@ -15,6 +15,7 @@ Steps:
A good example of this is an equation that does not factor nicely. If I know that $S_1$ is true, but I can't factor $S_2$ in a satisfactory way to prove that for each n+1 the statement is true, then proving a few until finding an instance of something factoring well can solve this issue.
+Can be used to prove [[FundamentalTheoremOfArithmetic.md]].
diff --git a/Unity.md b/Unity.md
@@ -11,7 +11,7 @@ Unity is a popular game engine, no duh.
**Aggregation:** Unity uses aggregation by grouping assets together (nesting)
-### Links
+### Components
[[MeshFilter.md]]
[[MeshRenderer.md]]
diff --git a/Index.md b/index.md
