identification of zero and infinity

Zero and infinity are often identified, that is, treated as synonymous, or used one in place of another. (This can be considered a case of circle-logic.) For example, specifying that a customer has a credit limit of 0 may well mean that the customer has infinite credit, that is, has no (thus ‘zero’) credit limit. The directive, by a robotic telephone system, ‘Press 9 to repeat these options.’ is a case of infinity (‘9’ in this case, ‘9’ being the digit greater than all other digits, and therefore ‘infinity’ with respect to them) taking you to 0 (that is, the beginning, where your options are listed for you). The ‘massively’ (i.e., practically ‘infinite’) multiplayer gave ‘Agar,io’ and Conway’s zero-player ‘game of life’ have similar playing environments. The function 1/(1/(x – x), having a null domain is intimately connected with the function f(x) = 0, having an infinite domain. The ranking of poker hands is from 0 (the highest – for five of a kind) to 9 (the lowest – for high card).