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I might be in over my head asking this question as I am only a rising sophomore in high school having just finished algebra 2, so I probably won't understand any complicated math concepts, but I'll try my best. Anyway, Recently I've been thinking about how addition is repeated incrementation, multiplication is repeated addition, exponentiation is rep. multiplication, tetration is rep. exponentiation, so on and so forth, and I was curious if it was possible for there to be operators in between. For example, if we used the notation +x to represent our operator, x=1 being addition, x=2 being multiplication and so on, what would +1.5 be? What would be the properties of it?

Robocittykat
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    Hi! Could any close-voters please explain to OP so they can improve the question? – Brian Tung Aug 02 '23 at 04:39
  • This part of the wikipedia article on tetration discusses exactly this issue. https://en.wikipedia.org/wiki/Tetration#Real_heights – Annika Aug 02 '23 at 04:50
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    This is an interesting question, but at this level of generality may be too vague for a non-subjective answer. Different people might interpret the analogy "1 is addition 2 is multiplication, what is 1.5?" in very different ways, and the question does not provide enough context to prefer any one way over any other. [As a side note, while "multiplication is repeated addition" and similar slogans are illustrative vibes, in some contexts they are not literally true; e.g. I know of no useful sense in which the product of real numbers $\pi \sqrt{2}$ is "$\pi$ added to itself, $\sqrt{2}$ times."] – leslie townes Aug 02 '23 at 05:24

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