Characterizations of the exponential function (original) (raw)
In mathematics, the exponential function can be characterized in many ways. The following characterizations (definitions) are most common. This article discusses why each characterization makes sense, and why the characterizations are independent of and equivalent to each other. As a special case of these considerations, it will be demonstrated that the three most common definitions given for the mathematical constant e are equivalent to each other.
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| dbo:abstract | In mathematics, the exponential function can be characterized in many ways. The following characterizations (definitions) are most common. This article discusses why each characterization makes sense, and why the characterizations are independent of and equivalent to each other. As a special case of these considerations, it will be demonstrated that the three most common definitions given for the mathematical constant e are equivalent to each other. (en) En matemáticas, la función exponencial se puede de muchas maneras. Las siguientes caracterizaciones (definiciones) son las más comunes. Este artículo explica por qué cada caracterización tiene sentido y por qué las caracterizaciones son independientes y equivalentes entre sí. Como un caso especial de estas consideraciones, veremos que las tres definiciones más comunes dadas para la constante matemática e también son equivalentes entre sí. (es) Nella matematica, la funzione esponenziale può essere caratterizzata in vari modi. Le seguenti definizioni sono le più comuni. Questo articolo discute il motivo per cui ogni caratterizzazione ha senso, e del perché ogni definizione implica l'altra. Come caso speciale di queste considerazioni, si vedrà che le tre definizioni più comuni della costante matematica e sono anche equivalenti tra di loro. (it) |
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| rdfs:comment | In mathematics, the exponential function can be characterized in many ways. The following characterizations (definitions) are most common. This article discusses why each characterization makes sense, and why the characterizations are independent of and equivalent to each other. As a special case of these considerations, it will be demonstrated that the three most common definitions given for the mathematical constant e are equivalent to each other. (en) En matemáticas, la función exponencial se puede de muchas maneras. Las siguientes caracterizaciones (definiciones) son las más comunes. Este artículo explica por qué cada caracterización tiene sentido y por qué las caracterizaciones son independientes y equivalentes entre sí. Como un caso especial de estas consideraciones, veremos que las tres definiciones más comunes dadas para la constante matemática e también son equivalentes entre sí. (es) Nella matematica, la funzione esponenziale può essere caratterizzata in vari modi. Le seguenti definizioni sono le più comuni. Questo articolo discute il motivo per cui ogni caratterizzazione ha senso, e del perché ogni definizione implica l'altra. Come caso speciale di queste considerazioni, si vedrà che le tre definizioni più comuni della costante matematica e sono anche equivalenti tra di loro. (it) |
| rdfs:label | Caracterizaciones de la función exponencial (es) Characterizations of the exponential function (en) Definizioni della funzione esponenziale (it) |
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