Justify Definition: Proofs - Meaning & Example

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In the context of proofs, "justify" means to provide a rigorous demonstration that supports a statement or theorem, rather than merely showing an example. Justification requires a comprehensive proof that holds true for all cases, rather than isolated instances. Terms like "substantiate" or "confirm" may imply support but do not equate to justification. Consequently, presenting an example alone is insufficient to justify a theorem. A clear understanding of this distinction is crucial in mathematical discourse.
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when dealing with proofs, what does the word "Justify" mean? does it mean show an example or prove for all cases?
 
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it means prove it. An example might "substantiate", or "confirm" a statement, or "lend credence" to it, but would not "justify" it.
 
so showing an example would not be enough to "justify" a therom?
 
i only answer each question once.
 
yeah, mathwonk kind of just answered that questoin
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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