Discusión:Significando

@Toad32767:¡Hola! ¿cómo estáis? Os escribo para preguntaros de dónde surge este término "significando": yo estudié ingeniería y las matemáticas que aprendí fueron rudas -e innecesariamente complejas para la profesión- y no hallo referencias o historias sobre este concepto. Este también es un aviso abierto para todo el que quiera involucrarse en esta conversación, os invito amablemente a disminuir mi ignoracia al respeto. Tened feliz cuarentena todas y todos.--Jimmy Olano (discusión) 12:39 28 abr 2020 (UTC)[responder]

Mantissa vs Significand (Mantisa y significando, términos distintos)[editar]

It is incorrect the fusion of the meanings mantissa and significand previously proposed, as we will see below. Let us explain first the proper meanings of Significant, significand and mantissa:

Definition 1. The first Significant digit of a real number x > 0 is the first digit

different from zero that appears in decimal expansion, e.g., the first significant digit of 301 and 0.301 is 3 in both cases. This definition is applicable to other digits.

In scientific notation, the significand of a real number is its coefficient when we express it in floating point, e.g., 20= 2*10 so its significand is 2.

Definition 2. The Significand S(x) of x> 0 ∈ ℝ is the unique real number such that, assuming base 10:

  x= S(x)*(10)^k where S(x) ∈ [1, 10), ∃k ∈ Z.

The order of magnitude, k, represents the number that more varies according to its absolute value. Remember that it is related to the first-digit, if we go now to the first-two digits the interval’s definition would change to S(x) ∈ ℝ is the unique real number such [10, 100).

In American English, what we have defined as Significand is erroneously denoted as mantissa, The “traditional” meaning of mantissa is:

Definition 3. The mantissa is the difference between the logarithm of a number and its integer part, log(x) – [log(x)], where if we represent the mantissa of thelogarithm base 10 of a number x by m(x), it has the following property:

m(x)= m(10x). That is, the mantissae are cyclic, circular data and can take valueson the unit circle centred at (0,0).

Therefore, the relationship between mantissa and significand lies in m(x)= log(S(x)). For example, for the explanation of Benford’s law this can lead to great confusion since many of the authors are of American origin and use the word "mantissa" when it is actually "significand"!

–All references in this paper to logarithms will be to the base 10 (applicable to other bases). --Naila Talavera (discusión) 02:34 14 abr 2021 (UTC)Naila Talavera[responder]