AMP STUDY NOTES
MAT2613 · REAL ANALYSIS
Complete Module
Cheatsheet
All seven chapters’ cheatsheets combined into a single volume, in
order, for the full module.
Chapter 1 — Preliminaries
Chapter 2 — The Real Numbers
Chapter 3 — Sequences
Chapter 4 — Series
Chapter 5 — Continuous Functions
Chapter 6 — Differentiation
Chapter 7 — Integration
CHEATSHEET · ALL CHAPTERS
Independent study material. Independently authored revision aid, not affiliated with, endorsed by, or sourced
from UNISA or any official assessment body. © AMP Study Notes.
,AMP STUDY NOTES
MAT2613 · REAL ANALYSIS
Chapter 1
Cheatsheet
Preliminaries — core rules, definitions, and a fast decision guide for
exam revision.
CHEATSHEET · CHAPTER 1
Independent study material. Independently authored revision aid, not affiliated with, endorsed by, or sourced
from UNISA or any official assessment body. © AMP Study Notes.
, AMP Study Notes — MAT2613 — Chapter 1 Cheatsheet
Chapter 1 Cheatsheet: Preliminaries
Core Rules
CONTRAPOSITIVE EQUIVALENCE
The converse is not automatically equivalent — only the contrapositive is.
NEGATION RULES
"for all , "→" , not "·" , " → "for all , not "·" and " → "not
or not "·" or " → "not and not "
SET OPERATIONS
INJECTIVE / SURJECTIVE / BIJECTIVE
Injective: . Surjective: (codomain fully hit). Bijective: both — inverse exists.
The Three Proof Methods
METHOD WHAT YOU ASSUME WHAT YOU SHOW
Direct true true, via a chain of deductions
Contrapositive false false
Contradiction The statement is false Some impossibility follows
Fast Decision Guide
IF THE QUESTION ASKS… REACH FOR…
"Prove is irrational" / "no integers satisfy…" Proof by contradiction.
"Prove if is even then is even" (statement about a Contrapositive proof.
consequence's negation being easier)
"Write the negation of…" Flip every "for all"/"there exists," flip "and"/"or," negate
the innermost condition.
Page 2 of 3
MAT2613 · REAL ANALYSIS
Complete Module
Cheatsheet
All seven chapters’ cheatsheets combined into a single volume, in
order, for the full module.
Chapter 1 — Preliminaries
Chapter 2 — The Real Numbers
Chapter 3 — Sequences
Chapter 4 — Series
Chapter 5 — Continuous Functions
Chapter 6 — Differentiation
Chapter 7 — Integration
CHEATSHEET · ALL CHAPTERS
Independent study material. Independently authored revision aid, not affiliated with, endorsed by, or sourced
from UNISA or any official assessment body. © AMP Study Notes.
,AMP STUDY NOTES
MAT2613 · REAL ANALYSIS
Chapter 1
Cheatsheet
Preliminaries — core rules, definitions, and a fast decision guide for
exam revision.
CHEATSHEET · CHAPTER 1
Independent study material. Independently authored revision aid, not affiliated with, endorsed by, or sourced
from UNISA or any official assessment body. © AMP Study Notes.
, AMP Study Notes — MAT2613 — Chapter 1 Cheatsheet
Chapter 1 Cheatsheet: Preliminaries
Core Rules
CONTRAPOSITIVE EQUIVALENCE
The converse is not automatically equivalent — only the contrapositive is.
NEGATION RULES
"for all , "→" , not "·" , " → "for all , not "·" and " → "not
or not "·" or " → "not and not "
SET OPERATIONS
INJECTIVE / SURJECTIVE / BIJECTIVE
Injective: . Surjective: (codomain fully hit). Bijective: both — inverse exists.
The Three Proof Methods
METHOD WHAT YOU ASSUME WHAT YOU SHOW
Direct true true, via a chain of deductions
Contrapositive false false
Contradiction The statement is false Some impossibility follows
Fast Decision Guide
IF THE QUESTION ASKS… REACH FOR…
"Prove is irrational" / "no integers satisfy…" Proof by contradiction.
"Prove if is even then is even" (statement about a Contrapositive proof.
consequence's negation being easier)
"Write the negation of…" Flip every "for all"/"there exists," flip "and"/"or," negate
the innermost condition.
Page 2 of 3
