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Yes, the graphs seem to be visual proof. And my rather wordy "proof" above was essentially saying what the graph would say. But that feels a little circumstantial to me and may or may not be solid enough proof to include it as a rather pivotal step in a larger proof (the crux of number theory being to avoid any ambiguity where you just never know, somewhere waaaaay out on the number line you might run across a weird hiccough in the procedings).
A little bit of hand waving is acceptable in proofs. You don't have to go back and prove that 2>1 every time you start a proof. And I know this one is pretty trivial. I'm just not well versed in the theory enough to know if it's trivial enough for me to get away with leaning on some higher level concepts (exponential and linear growth) rather than formally proving the nuts and bolts.
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'He who receives an idea from me, receives instruction himself without lessening mine; as he who lights his taper at mine, receives light without darkening me.'
-TJ
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