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Can the existence of a mathematical entity be proved…

“Can the existence of a mathematical entity be proved without defining it ?” quote by Jacques Hadamard
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“Can the existence of a mathematical entity be proved without defining it ?”

Jacques Hadamard

About This Quote

This interpretation was drafted with AI assistance. It is one reading of the quote, not the author's own explanation.

Mathematical existence proofs may require definitions to be precise.

In simple terms: Existence needs definition.

Key Takeaway

Define before proving.

Themes

mathematics logic definition

Mood

analytical curious

Type

philosophical academic

When to use this quote

  • research
  • teaching
  • theoretical work

Key Concepts

philosophy of math foundations

Questions to Reflect On

  • Can we accept undefined objects?
  • What role do definitions play in proof?
A Different Perspective

Some entities can be inferred indirectly.

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