## Math: Pythagorean triples and Fermat’s Last Theorem

Tutoring math, ideas are always important. The tutor mentions Fermat’s Last Theorem. A Pythagorean triple is a set of three integers that satisfy a2+b2=c2 There are infinite Pythagorean triples. However, there are no corresponding sets of integers for higher n: …

## Math: set subtraction

Tutoring math, ideas can always be revisited. The tutor mentions set subtraction. Set subtraction is different from arithmetic subtraction. If A and B are sets, the operation A-B ignores what’s in B only; it just gives back what’s present in …

## Math: surjection

Tutoring math, definitions can be interesting. The tutor mentions surjection. In my previous post I mention codomain and its relation to the range. Now I continue with surjection. A function is a surjection, or surjective, if and only if its …

## Math: codomain vs range

Tutoring math, definitions are important. The tutor mentions a couple. The codomain of a function is the set of its possible outputs, while its range is the set that actually is output. Let’s imagine you plan to measure the mass …

## Math: a detail about order of operations

Tutoring math, so often a detail can pose danger. The tutor relates such a case. Occasionally, regarding order of operations, I’ve heard people say you do addition before subtraction, since of course in BEDMAS, A comes before S. It’s a …

## Math: break-even year-over-year

Self-tutoring about math: the tutor mentions perhaps an oft-considered question. Suppose an investment loses x% this year. What percent does the resulting sum need to gain next year in order to break even? Imagine an investment of initial value \$250. …

## Calculator use: when adding isn’t associative(?)

Tutoring math, curiosities can arise. The tutor mentions a calculator one. In front of me are two reliable scientific calculators from different manufacturers. Both give the following results: 2+1exp20-1exp20 = 0 but 2+(1exp20-1exp20)=2 1exp20 means scientific notation: 1×1020. How can …

## Math: idempotent

Tutoring math, terms can be interesting. The tutor mentions idempotent. idempotent (adj): repeatable without further result, or unchanged by repetition of an operation. Source: encylopediaofmath.org

## Math: bacon and eggs

Tutoring math, you face real-life scenarios. The tutor mentions an example. Suppose one egg and two strips of bacon contain 13.5g protein, but two eggs and one strip of bacon contain 16.5g protein. How much in each? Let x be …

## Math: increase then decrease by same percentage, or vice-versa

Tutoring math, you run into curiosities. The tutor mentions one with percentage. If an amount is increased, then decreased, by the same percentage, the net effect is shrinkage, regardless of which happens first. Let the amount be 100. Furthermore, for …