inversambisignum

Inversambisignum (noun): The ∓ symbol, commonly called the minus-or-plus sign or minus-plus sign. The name derives from Latin: inversa ("inverted" or "turned upside down"), ambi- ("both" or "on both sides"), and signum ("sign" or "symbol"), and reflects its role as the counterpart to the ± symbol (ambisignum).

Meaning and Use

1) Relationship to ± (ambisignum):

• ∓ appears with ± to denote symmetrical or complementary values in equations.
• The top sign of ± corresponds to the top sign of ∓, and the bottom sign of ± to the bottom sign of ∓.
• Example: In a ± b ∓ c:

◦ First case: a + b − c

◦ Second case: a − b + c.

2) Applications:

• Quadratic equations: Specifies dual results involving radicals.
• Physics and Engineering: Models symmetry (e.g., waveforms, alternating currents).
• Complex numbers: Describes conjugate pairs with opposite-sign components.

Why It Is Necessary

Without ∓, expressions with multiple operations could be ambiguous. Paired ± and ∓ ensure clarity by mirroring opposing effects.

Mnemonic: Think of ± as "positive then negative" and ∓ as "negative then positive," balancing dual relationships.

Note: it is tautological to refer to an 'inversambisignum sign' or an 'inversambisignum symbol' in the same way that it is tautological to refer to RAS syndrome (where RAS means 'redundant acronym syndrome')...

As a physicist Carl used the ambisignum almost daily in his writing, but it was a rare occasion indeed when his formulæ required the use of an inversambisignum.