Formal Sciences
What is a set?
A set groups well-defined objects; membership, inclusion and operations describe its structure.
8 min readDiscover
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Computer Science
Algorithms: specify, execute and justify a maximum search
From contract to proof: follow a maximum search, test its limits and distinguish method, program, correctness and termination.
25 min readDiscover
Social Sciences
The law of diminishing returns
With technology unchanged, increasing one input while the others remain fixed often ultimately reduces its marginal product; if it is the only variable input, paid at a constant price, and as long as its marginal product remains positive, this decline raises marginal cost.
15 min readDiscover
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Showing 22 of 22 results
Computer Science
Algorithms: specify, execute and justify a maximum search
From contract to proof: follow a maximum search, test its limits and distinguish method, program, correctness and termination.
25 min readRead
Formal Sciences
Understanding the derivative: limit, tangent, and instantaneous change
A derivative measures instantaneous change: it arises as the limit of rates of change and is interpreted as the slope of a tangent.
18 min readRead
Formal Sciences
Rate of change: measuring change over an interval
Rate of change measures average change between two specified inputs. See how interval choice, units, and representation determine what the number actually means.
14 min readRead
Formal Sciences
Functions: domain, outputs, preimages, and representations
A function is more than a formula: each allowed input has exactly one output. Distinguish domain, image, preimages, and the main representations of the same rule.
12 min readRead
Formal Sciences
What is a set?
A set groups well-defined objects; membership, inclusion and operations describe its structure.
8 min readRead
Formal Sciences
Graphs, degrees, and Eulerian trails
In a multigraph whose vertices of nonzero degree are all connected, degree parity determines whether every edge can be traversed exactly once.
11 min readRead
Social Sciences
The law of diminishing returns
With technology unchanged, increasing one input while the others remain fixed often ultimately reduces its marginal product; if it is the only variable input, paid at a constant price, and as long as its marginal product remains positive, this decline raises marginal cost.
15 min readRead
Social Sciences
Comparative advantage
In the two-good, constant-cost model, reallocation follows opportunity cost; if preferences are strictly increasing in chairs over the bundles compared, a price strictly between the two costs enables mutual gain.
16 min readRead
Finance
The time value of money
An amount means nothing without its date. Comparing sums placed at different dates requires bringing them back to a single date: a flow weighs the less the more distant its maturity, as soon as the reference return is positive.
8 min readRead
Finance
Compound interest
When interest is added to the principal, it in turn earns interest: the sum no longer grows by a fixed amount each period, it is multiplied by a fixed factor.
7 min readRead
Social Sciences
Supply and Demand
Supply and demand are not quantities but two relations between price and quantity; their intersection defines the equilibrium price.
7 min readRead
Social Sciences
Opportunity Cost
The cost of a choice is not limited to the money spent: it is the value of the best option it makes you give up.
5 min readRead
Formal Sciences
Real analysis
All of analysis rests on a single property: the completeness of ℝ. Remove it, and its theorems fall one by one.
7 min readRead
Natural Sciences
Conservation of energy
The energy of an isolated system does not change; only its form does, and this invariance follows from a symmetry.
6 min readRead
Formal Sciences
Induction
Induction proves infinitely many statements with two checks: a starting point, and a step that propagates.
6 min readRead
Formal Sciences
Inference
To infer is to pass from premises to a conclusion by a rule; the rule is judged on its form, not on the content.
6 min readRead
Formal Sciences
The predicate
A predicate is a statement with a hole: it becomes true or false only once the hole is filled, or quantified.
6 min readRead
Formal Sciences
Probability
A probability is a measure between 0 and 1 on events; three axioms suffice to derive everything else.
6 min readRead
Formal Sciences
The limit
A limit says what a function tends towards at a point, without needing to be defined there.
6 min readRead
Formal Sciences
The real number
A real number is a point on the continuous line; what sets it apart from a rational is that it leaves no gap.
6 min readRead
Formal Sciences
What is a digit?
A digit is a symbol used to write numbers; a base uses exactly as many digits as its value.
4 min readRead
Formal Sciences
What is an even number?
An even number is an integer divisible by 2 with no remainder.
3 min readRead