Education5 min read
Predicates and Quantifiers: Reading ∀ and ∃ Without Getting Lost
What predicates, the universal quantifier ∀ and the existential quantifier ∃ mean, how the domain changes a statement's truth, and why order matters.
383 articles · page 5 of 16
Education guides, page 5
Articles 97–120 of 383, newest first. The introduction to this reading list, its topic hubs and the guides other articles cite most are on the first page.
Education articles 97–120
- Education5 min read
Proof by Contradiction: How It Works and When to Reach for It
Proof by contradiction assumes the statement is false and derives an impossibility. Why it is valid, four worked proofs, and how to write the first line.
- Education4 min read
Proof by Contrapositive: The Indirect Proof That Is Often Easiest
To prove 'if p then q', prove 'if not q then not p' instead. Why it is valid, how to write one, five worked examples and how to tell it is the right method.
- Education4 min read
Proof by Induction, Step by Step: Base Case, Hypothesis and the Inductive Step
How to write a proof by induction: the base case, the inductive hypothesis and the step that uses it, with worked sum, divisibility and inequality proofs.
- Education4 min read
Reflexive, Symmetric, Antisymmetric, Transitive: Checking a Relation's Properties
How to test a relation for the four key properties using its list of pairs, its matrix or its directed graph, with worked examples and the antisymmetry traps.
- Education4 min read
Ramsey Numbers: Why R(3,3) = 6
In any group of six people, three are mutual friends or mutual strangers. The proof, why five is not enough, and why Ramsey numbers are so hard to compute.
- Education5 min read
Recurrence Relations: Setting Them Up and Solving the Linear Ones
How to model a problem with a recurrence relation and solve linear ones with constant coefficients, including repeated roots and a constant extra term.
- Education3 min read
Risk Tolerance and Time Horizon: Questions to Ask Before Any Investment
Risk tolerance is your ability and willingness to lose money for higher potential returns. How time horizon changes it, a drawdown test and questions to ask.
- Education5 min read
Roman Republic vs Roman Empire: What Changed and When
The Roman Republic and Roman Empire compared: consuls and Senate versus a princeps, why 27 BC is the usual dividing line, and what Augustus kept and changed.
- Education4 min read
The RSI Indicator: How It Is Calculated and Why "Overbought" Is Not a Forecast
The Relative Strength Index compares recent gains with recent losses on a 0–100 scale. How Wilder's RSI is calculated and why overbought is not a sell signal.
- Education4 min read
Rules of Inference: Modus Ponens, Modus Tollens and the Rest, with Worked Arguments
The rules of inference used in discrete math, from modus ponens to resolution and the quantifier rules, with a numbered derivation and the fallacies to avoid.
- Education4 min read
Sigma Notation and Sums: Reading, Splitting and Proving Summation Formulas
How to read Σ notation, the rules for splitting and shifting sums, the standard closed forms, telescoping sums, and how to prove a sum formula.
- Education4 min read
Set Operations Explained: Union, Intersection, Difference and Complement
Union, intersection, difference, complement and symmetric difference, each defined with a Venn picture and a worked example, plus how to prove set identities.
- Education4 min read
How Short Selling Works, and Why Its Losses Have No Ceiling
Short selling means selling borrowed shares and buying them back later. How a short sale works step by step, its costs, and why its losses are unlimited.
- Education3 min read
What SIPC Protection Covers, and What It Does Not
SIPC protects up to $500,000 per customer, including $250,000 cash, if a member brokerage fails. It does not cover market losses. Limits and examples.
- Education4 min read
Stars and Bars: Counting Combinations with Repetition
How the stars and bars method counts ways to share identical items among distinct groups, with and without minimums, and why the formula is C(k + n − 1, n − 1).
- Education5 min read
Stock Buybacks: How Repurchases Work and What They Change
A buyback is a company purchasing its own shares. Methods, the effect on earnings per share, the SEC Rule 10b-18 safe harbor and the 1% US excise tax.
- Education4 min read
Stock Market Hours, Pre-Market and After-Hours Trading Explained
US stock market hours are 9:30 a.m. to 4:00 p.m. Eastern. What pre-market, after-hours and overnight sessions are, and why trading in them carries extra risk.
- Education3 min read
Stock Splits and Reverse Splits: Why the Price Changes but Your Stake Does Not
A stock split multiplies shares and divides the price; a reverse split does the opposite. Why neither changes what you own, and why companies do them.
- Education3 min read
Stocks vs Bonds: Ownership vs Lending, and How Their Risks Differ
A stock is a share of ownership; a bond is a loan to an issuer. How each pays you, who is paid first in a bankruptcy, interest rate risk and how they combine.
- Education4 min read
Stop Orders vs Stop-Limit Orders: What Happens When the Price Gaps
A stop order turns into a market order at the stop price; a stop-limit turns into a limit order. How each behaves in a fast or gapping market, with examples.
- Education5 min read
Strong Induction vs Ordinary Induction: When You Need More Than One Step Back
Strong induction assumes every earlier case, not just the last. When you need it, why it is valid, and worked proofs with stamps, primes and Fibonacci numbers.
- Education4 min read
Support and Resistance: Price Levels, Hindsight and Why They Fail
Support and resistance are price levels where falling or rising prices have tended to stall. How chart readers draw them, role reversal, and why levels break.
- Education4 min read
Tautology, Contradiction or Contingency? How to Tell in One Truth Table
A tautology is always true, a contradiction always false and a contingency depends on its parts. How to classify any statement, with worked truth tables.