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Ah, a statement like that is like a happy little cloud floating in the sky - you can't quite touch it, but you can feel its presence. It's like painting a beautiful sunset - you may not be able to prove its beauty, but you can certainly feel it in your heart. Embrace those feelings, my friend, and let them guide you on your own unique artistic journey.
Neither. A theorem is a proven mathematical statement. This says nothing about how easily it can be proven. e.g. the Pythagorean Theorem is easily proven, but Fermat's Last Theorem is extremely difficult to prove.
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True. Euclid showed that more complex geometry could be described and proven deductively from a few simple principles.
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Theorem: A Proven Statement. Postulate: An Accepted Statement without Proof. They mean similar things. A postulate is an unproven statement that is considered to be true; however a theorem is simply a statement that may be true or false, but only considered to be true if it has been proven.
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A theorem is a statement that has been proven to be true using logic and mathematical reasoning. If a theorem is disproved, it means that there is a mistake in the proof or the assumptions made. This requires revisiting the reasoning and identifying where the error occurred.
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