identity
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identity
The totality of the characteristics that make a person or thing unique and distinguishable from others; the essence of a person.
Der Detektiv musste die wahre Identität des Zeugen geheim halten.
The detective had to keep the witness's true identity secret.
identity
In mathematics, an equation that is true for all possible values of the variables.
Die binomische Formel (a+b)² = a² + 2ab + b² ist eine mathematische Identität.
The binomial formula (a+b)² = a² + 2ab + b² is a mathematical identity.
'Identität' (identity) belongs to a word family with the adjective 'identisch' (identical) and the verb 'identifizieren' (to identify someone or something). These words share the stem 'ident-'.
Die Polizei konnte den Mann anhand seines Ausweises identifizieren.
The police were able to identify the man using his ID.
In connection with personality, 'Identität' (identity) is often used with verbs like 'feststellen' (to establish), 'prüfen' (to check), 'verbergen' (to hide), or 'preisgeben' (to reveal).
Der Zeuge wollte seine Identität nicht preisgeben.
The witness did not want to reveal his identity.
The word 'Identität' (identity) is often used in official or formal contexts, for example with the police, in government offices, or in academic discussions.
Für den Vertrag ist die Feststellung der Identität beider Parteien notwendig.
For the contract, establishing the identity of both parties is necessary.
You can recognize the mathematical meaning from the context. If 'Formeln' (formulas), 'Gleichungen' (equations), 'Variablen' (variables), or other mathematical terms are being discussed, this special meaning is intended.
In der Prüfung mussten wir eine trigonometrische Identität beweisen.
In the exam, we had to prove a trigonometric identity.
equation
An Identität and a Gleichung both connect mathematical terms with an equals sign. However, an Identität is true for all permitted values of the variables, whereas a Gleichung may be true only for certain values. Use Identität for a general truth and Gleichung for a specific relationship.
x² + 2x + 1 = (x + 1)² ist eine Identität, weil sie für jeden zulässigen Wert von x gilt.
x² + 2x + 1 = (x + 1)² is an identity because it holds for every permitted value of x.
2x + 3 = 9 ist eine Gleichung, die nur für x = 3 stimmt.
2x + 3 = 9 is an equation that is true only when x = 3.
