Finesentence mobile logo
Sign in Login / Register

Undifferentiable Meaning: Definition, Examples, and Translations

📈
Add to dictionary

undifferentiable

[ˌʌnˌdɪfəˈrɛnʃəbəl ]

Definition

Context #1 | Adjective

mathematics

Not capable of being distinguished or differentiated from something else. In calculus, a function is considered undifferentiable at a certain point if its derivative does not exist at that point.

Synonyms

indifferentiable, indistinguishable, non-differentiable.

Which Synonym Should You Choose?

arrow down
Word Description / Examples
undifferentiable

Used in mathematics to describe a function that does not have a derivative. It is a technical term and is not often used in everyday language.

  • This function is undifferentiable at x=0.
  • Researchers are studying undifferentiable points to better understand the behavior of complex functions.
indistinguishable

Used to describe things that cannot be told apart either visually, audibly, or in another sense. Commonly used in everyday language.

  • The twins were indistinguishable from each other.
  • The copies are indistinguishable from the original.
indifferentiable

Rarely used and mostly found in mathematical contexts, similar to 'undifferentiable'. It means not capable of being differentiated.

  • The equation provided was deemed indifferentiable at multiple points.
  • Some mathematical problems are indifferentiable in nature.
non-differentiable

Primarily used in mathematics, often interchangeably with 'undifferentiable'. It describes a function that does not have a derivative at a specific point or interval.

  • The function is non-differentiable at x=2.
  • Non-differentiable functions present a unique challenge in calculus.

Examples of usage

  • The function |x| is undifferentiable at x=0.
  • The concept of undifferentiability plays a key role in the study of continuity and differentiability in mathematics.

Translations

To see the translation, please select a language from the options available.

Interesting Facts

Mathematics

  • In calculus, a function is undifferentiable at a point if it doesn't have a smooth tangent, like a sharp corner.
  • A classic example of an undifferentiable function is the absolute value function at zero, creating a 'V' shape.
  • This concept is crucial in understanding limits and continuity in mathematical analysis.

Philosophy

  • The concept questions how we understand change and difference within existentialism, focusing on identity.
  • Philosophers often discuss how certain states of being might appear undifferentiable in our perception of reality.

Computer Science

  • In machine learning, certain models may act as undifferentiable functions where direct optimization isn't possible.
  • Understanding when functions are undifferentiable helps in adapting algorithms for efficient learning.

Physics

  • In quantum mechanics, certain states are described as undifferentiable due to the indistinguishability of particles.
  • This aligns with the uncertainty principle, where the precise attributes of particles cannot be fully determined.

Art

  • In abstract art, the undifferentiable nature of some pieces leaves interpretation open to the viewer's perspective.
  • Artists sometimes use blending techniques that create undifferentiable regions, challenging our ideas of form.

Origin of 'undifferentiable'

The word 'undifferentiable' originates from the prefix 'un-' meaning 'not' and 'differentiable' from the verb 'differentiate', which comes from the Latin word 'differentiatus', past participle of 'differentiare', meaning 'to distinguish'. The term is commonly used in mathematics to describe functions that are not differentiable at certain points.