- #1
hddd123456789
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Hey guys, let's say I were to define a new mathematical object, a novel type of number for example, and I am trying to determine its various properties (arithmetic, exponential, logarithmic, etc). Now, let's say I am able to use these numbers to produce solutions that agree with expected results. Would this lend any sort of weight towards the formal existence of said numbers, or is a formal proof required to be taken seriously?
I don't mean to be vague, but really, how does one "show" that a new type of number exists? How was it done for imaginary numbers? Were they just a novelty until someone saw that they had real world meaning in engineering?
Many thanks!
Edit: If still too general and/or vague, book recommendations will also be appreciated :)
I don't mean to be vague, but really, how does one "show" that a new type of number exists? How was it done for imaginary numbers? Were they just a novelty until someone saw that they had real world meaning in engineering?
Many thanks!
Edit: If still too general and/or vague, book recommendations will also be appreciated :)