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When we see a problem containing addition, we usually visualize it using a number line or containing quantities of some sorts. Does this meaning of the addition operator as combining quantities, or extending a length arise because of how we defined addition to be, or did it arise based on how we "felt" addition should work?

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    "We" defined addition based on how we "felt" it should work. The number line visualization is fairly late historically, but counts and measures of combined items, including line segments, is what "addition" was abstracted from. – Conifold Jul 20 at 4:13
  • @Conifold, why not post this as an answer? – niels nielsen Jul 20 at 5:02
  • Yes, the "meaning" of addition is the combination of quantities (assuming that the meaning of "combination of things" is already known) – Mauro ALLEGRANZA Jul 20 at 6:32
  • There is an interesting book "Mathematics from the birth of numbers" written by a M.D. turned math enthusiast who has done extensive research into mathematics. He goes into the origin of numbers among various cultures and early forms of addition. You may find it interesting. – Rob Jul 21 at 14:12

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