the.com/demonstration

Proof you perform, because telling people is cheaper than showing them, but less convincing.

means A public display, protest, or practical proof that shows something is true or how something works by actually doing it, rather than just claiming it.

from From Latin demonstrare — de- ('completely, thoroughly') plus monstrare ('to show, point out'), the same monstrare that gives us 'monster' (originally a thing pointed out as an omen). So a demonstration is literally a thorough pointing-out: not just telling, but showing so plainly no one can look away.

etymology
from latin demonstrare, to point out thoroughly
math usage
a proof, not just a protest
sales version
called a demo, trust optional
civic version
a crowd pointing out something thoroughly too
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