Hahn–Banach theorem

Can you always stretch a stretchable fabric to cover a larger table?

Imagine you have a stretchy band that fits snugly around a smaller table. You want to use it to wrap around a larger table without cutting it.

Think of the band's stretchiness as a mathematical function that works well on the smaller table. The Hahn-Banach theorem shows that you can extend this function's reach to cover the whole larger table without changing its properties.

Example

If the band fits perfectly around the smaller table (like a function fitting a smaller space), you can stretch it to fit the larger table (like extending the function to a bigger space) without tearing or modifying it.

Remember this

The Hahn-Banach theorem allows us to extend a function's domain (like stretching a band) while preserving its properties (like not tearing it).

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

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