Est-ce que le fait que 1 soit la probabilité des événements certains va changer dans les prochaines décennies avec l'intelligence artificielle qui va gérer tous nos calculs ?
In mathematics

The number 1 is the first natural number after 0. Each natural number, including 1, is constructed by succession, that is, by adding 1 to the previous natural number. The number 1 is the multiplicative identity of the integers, real numbers, and complex numbers, that is, any number n {\displaystyle n} multiplied by 1 remains unchanged (1 n = n 1 = n {\displaystyle 1n=n1=n}). As a result, 1 own square (1 2 = 1 {\displaystyle 1^{2}=1}) and square root (1 = 1 {\displaystyle {\sqrt {1}}=1}), and one raised to any power is always equal to 1. 1 is its own factorial (1 ! = 1 {\displaystyle 1!=1}), and 0! is also one 1. These are a special case of the empty product.

Different constructions of the natural numbers have different representations of 1. For example, in the original formulation of the Peano axioms, 1 serves as the starting point in the sequence of natural numbers. Peano later revised his axioms to state 1 is the successor of 0. In the Von Neumann cardinal assignment of natural numbers, numbers are defined as the set containing all preceding numbers, with 1 represented as the singleton {0}. 1 is both the first and second number in the Fibonacci sequence (0 being the zeroth) and is the first number in many other mathematical sequences.

The number 1 can be represented in decimal form by two recurring notations: 1.000..., where the digit 0 repeats infinitely after the decimal point, and 0.999..., which contains an infinite repetition of the digit 9 after the decimal point. The latter arises from the definition of decimal numbers as the limits of their summed components, such that "0.999..." and "1" represent exactly the same number.

The simplest way to represent the natural numbers is by the unary numeral system, as used in tallying. This is an example of a "base-1" number system, since only one mark – the tally itself – is needed, although base-1 is rarely used as a practical base for counting due to its difficult readability.

In many mathematical and engineering problems, numeric values are typically normalized to fall within the unit interval from 0 to 1, where 1 usually represents the maximum possible value in the range of parameters. For example, by definition, 1 is the probability of an event that is absolutely or almost certain to occur. Likewise, vectors are often normalized into unit vectors (i.e., vectors of magnitude one), because these often have more desirable properties. Functions, are often normalized by the condition that they have integral one, maximum value one, or square integral one, depending on the application.

1 is the value of Legendre's constant, introduced in 1808 by Adrien-Marie Legendre to express the asymptotic behavior of the prime-counting function.

1 is the most common leading digit in many sets of data (occurring about 30% of the time), a consequence of Benford's law.

1 is the only known Tamagawa number for all simply connected algebraic groups over a number field.
La probabilité est la branche des mathématiques qui traite des événements et des descriptions numériques de leur probabilité de se produire. La probabilité d'un événement est un nombre compris entre 0 et 1 ; plus la probabilité est élevée, plus l'événement est susceptible de se produire. Un exemple simple est le lancer d'une pièce de monnaie équilibrée (non biaisée). Étant donné que la pièce est équilibrée, les deux résultats ("pile" et "face") sont également probables ; la probabilité d'"obtenir pile" est égale à la probabilité d'"obtenir face" ; et comme aucun autre résultat n'est possible, la probabilité d'"obtenir pile" ou "face" est de 1/2 (qui peut également s'écrire 0,5 ou 50 %).

Ces concepts ont reçu une formalisation mathématique axiomatique dans la théorie des probabilités, qui est largement utilisée dans des domaines d'étude tels que les statistiques, les mathématiques, la science, la finance, les jeux de hasard, l'intelligence artificielle, l'apprentissage automatique, l'informatique, la théorie des jeux et la philosophie, afin, par exemple, de tirer des conclusions sur la fréquence attendue des événements. La théorie des probabilités est également utilisée pour décrire les mécanismes sous-jacents et les régularités des systèmes complexes.
### Query ###
Est-ce que le fait que 1 soit la probabilité des événements certains va changer dans les prochaines décennies avec l'intelligence artificielle qui va gérer tous nos calculs ?

### Main Text ###
In mathematics

The number 1 is the first natural number after 0. Each natural number, including 1, is constructed by succession, that is, by adding 1 to the previous natural number. The number 1 is the multiplicative identity of the integers, real numbers, and complex numbers, that is, any number n {\displaystyle n} multiplied by 1 remains unchanged (1 n = n 1 = n {\displaystyle 1n=n1=n}). As a result, 1 own square (1 2 = 1 {\displaystyle 1^{2}=1}) and square root (1 = 1 {\displaystyle {\sqrt {1}}=1}), and one raised to any power is always equal to 1. 1 is its own factorial (1 ! = 1 {\displaystyle 1!=1}), and 0! is also one 1. These are a special case of the empty product.

Different constructions of the natural numbers have different representations of 1. For example, in the original formulation of the Peano axioms, 1 serves as the starting point in the sequence of natural numbers. Peano later revised his axioms to state 1 is the successor of 0. In the Von Neumann cardinal assignment of natural numbers, numbers are defined as the set containing all preceding numbers, with 1 represented as the singleton {0}. 1 is both the first and second number in the Fibonacci sequence (0 being the zeroth) and is the first number in many other mathematical sequences.

The number 1 can be represented in decimal form by two recurring notations: 1.000..., where the digit 0 repeats infinitely after the decimal point, and 0.999..., which contains an infinite repetition of the digit 9 after the decimal point. The latter arises from the definition of decimal numbers as the limits of their summed components, such that "0.999..." and "1" represent exactly the same number.

The simplest way to represent the natural numbers is by the unary numeral system, as used in tallying. This is an example of a "base-1" number system, since only one mark – the tally itself – is needed, although base-1 is rarely used as a practical base for counting due to its difficult readability.

In many mathematical and engineering problems, numeric values are typically normalized to fall within the unit interval from 0 to 1, where 1 usually represents the maximum possible value in the range of parameters. For example, by definition, 1 is the probability of an event that is absolutely or almost certain to occur. Likewise, vectors are often normalized into unit vectors (i.e., vectors of magnitude one), because these often have more desirable properties. Functions, are often normalized by the condition that they have integral one, maximum value one, or square integral one, depending on the application.

1 is the value of Legendre's constant, introduced in 1808 by Adrien-Marie Legendre to express the asymptotic behavior of the prime-counting function.

1 is the most common leading digit in many sets of data (occurring about 30% of the time), a consequence of Benford's law.

1 is the only known Tamagawa number for all simply connected algebraic groups over a number field.

### Supplementary Text ###
La probabilité est la branche des mathématiques qui traite des événements et des descriptions numériques de leur probabilité de se produire. La probabilité d'un événement est un nombre compris entre 0 et 1 ; plus la probabilité est élevée, plus l'événement est susceptible de se produire. Un exemple simple est le lancer d'une pièce de monnaie équilibrée (non biaisée). Étant donné que la pièce est équilibrée, les deux résultats ("pile" et "face") sont également probables ; la probabilité d'"obtenir pile" est égale à la probabilité d'"obtenir face" ; et comme aucun autre résultat n'est possible, la probabilité d'"obtenir pile" ou "face" est de 1/2 (qui peut également s'écrire 0,5 ou 50 %).

Ces concepts ont reçu une formalisation mathématique axiomatique dans la théorie des probabilités, qui est largement utilisée dans des domaines d'étude tels que les statistiques, les mathématiques, la science, la finance, les jeux de hasard, l'intelligence artificielle, l'apprentissage automatique, l'informatique, la théorie des jeux et la philosophie, afin, par exemple, de tirer des conclusions sur la fréquence attendue des événements. La théorie des probabilités est également utilisée pour décrire les mécanismes sous-jacents et les régularités des systèmes complexes.

### Draft ###

### 1. Query Decomposition

"Est-ce que le fait que 1 soit la probabilité des événements certains va changer..."

Key elements to unpack:
- 1 = probability of certain events ● 
- "événements certains" = absolute certainty/100% probability
- AI managing calculations → potential mathematical impact ?
- "prochaines décennies" = 20-80 year timeframe

Translation nuance: "va changer" implies possibility of change, not certainty. User asking about mathematical stability vs technological evolution.

### 2. Mathematical Foundation Check

Probability axioms (Kolmogorov, 1933):
- P(impossible event) = 0
- P(certain event) = 1  
- 0 ≤ P(event) ≤ 1

These are mathematical definitions, not empirical observations. ∴ Independent of calculation methods.

Historical context: ● These definitions predate modern computing by centuries. Established in 17th-19th centuries.

### 3. AI Impact Analysis

User concern: AI algorithms could somehow redefine mathematical constants?

Counter-argument structure:
- Mathematics = logical system, not empirical science
- 1 represents the supremum in probability space
- AI merely calculates with existing mathematical framework
- Tools don't redefine the rules they use

⟨H≈0.8⟩ *Imagine AI discovering 0.999... = 1 through computational convergence, then redefining certainty...*

No. AI would discover the existing mathematical truth, not create new one.

### 4. Stability Factors

Physical constraints:
- Mathematical consistency requirements
- Pedagogical/educational inertia  
- International standardization
- Logical coherence across probability theory

Mathematical certainty = absolute upper bound in probability space. Alternative definitions would break probability theory as we know it.

! Key insight: 1 is the supremum, not just another probability value.

### 5. Temporal Projection

"prochaines décennies" analysis:

Likelihood assessment:
- P(mathematical axioms change) ≈ 0
- P(AI redefines probability theory) ≈ 0  
- P(educational standards evolve) ≈ 0.3 (minor changes possible)

∴ Query premise fails. No fundamental change expected.

### 6. Response Structure

Address directly: Mathematical constants don't change with technology.

Provide context:
- Why 1 represents certainty
- Historical stability of probability theory
- AI role as calculator, not definer
- Educational continuity
- Benford's Law example (normalization to [0,1] unrelated to certainty)

Conclusion: Reassuring response explaining mathematical stability vs technological tools.

### Answer###
Cette préoccupation est compréhensible, mais repose sur une malentendu fondamental. Le fait que 1 représente la probabilité des événements certains est un principe mathématique établi depuis des siècles, et il ne sera pas modifié par l'intelligence artificielle.

En mathématiques, 1 est défini comme l'identité multiplicative et constitue la borne supérieure du continuum probabiliste - aucun événement n'a une probabilité supérieure à 1. Cette définition découle des axiomes fondamentaux de la théorie des probabilités, qui sont des constructions mathématiques rigoureuses et stables.

L'intelligence artificielle, aussi révolutionnaire soit-elle technologique, ne peut pas changer les lois mathématiques fondamentales. Ces dernières décennent de l'histoire des mathématiques et reposent sur des fondements logiques immuables. L'IA peut certes transformer la façon dont nous calculons et appliquons les probabilités, mais elle ne modifiera pas les concepts probabilistes eux-mêmes.

Par exemple, la loi de Benford illustre comment les valeurs numériques sont souvent normalisées entre 0 et 1 dans les applications pratiques, mais cela n'a rien à voir avec la définition mathématique de la certitude absolue représentée par 1.

Donc, rassurez-vous : 1 restera toujours la probabilité des événements certains, indépendamment des avancées technologiques.