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I'm wondering if there are logical meanings for the mathematical operations (addition, subtraction, multiplication, and division) , from the perspective of each operand?

Michael Shenouda
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  • In $\mathbb{F}_2 = ℤ/2ℤ$, if you interpret zero as false and one as true, “$+$” (and “$-$”) corresponds to exclusive or and “$·$” corresponds to and. – k.stm Apr 08 '14 at 08:36
  • See Boolean algebra – Mauro ALLEGRANZA Apr 08 '14 at 08:36
  • I will propose some ideas: – Michael Shenouda Apr 08 '14 at 08:46
  • if we have two persons, the first's length = 8, and the second 's length = 2, now if the first looked to the second , then the perception of the first to the second should be that the second is more little than he's really is , and the other way, if the second looked to the first , then the first will be percepted as taller than he's really is. – Michael Shenouda Apr 08 '14 at 08:57
  • now if any one looks to him self then the perception is going to be normal, not taller not smaller – Michael Shenouda Apr 08 '14 at 08:59
  • that was the logic part, now for the mathematical part, – Michael Shenouda Apr 08 '14 at 09:01
  • 8 / 2 = 4, 2 / 8 = 1 / 4, 2 / 2 = 1 or 8 / 8 = 1 – Michael Shenouda Apr 08 '14 at 09:03
  • the logical interpretation: 8 to 2 is more than normal i.e: 4 > 1, 2 to 8 is less than normal i.e: 1/4 < 1, and the 2 to 2 is normal i.e: 1 – Michael Shenouda Apr 08 '14 at 09:12
  • now for how to use it : if we have a problem which include as given ... something is w.r.t something else = some quantity, then that should be modeled as second something / first something = quantity – Michael Shenouda Apr 08 '14 at 09:18
  • now, i need some mathematician to tell me if all of this feasible or not, and if so , how to develop it to ease the understanding of mathematics, because I'm too too too weak in mathematics – Michael Shenouda Apr 08 '14 at 09:21
  • But we already have the "less than" and "greater than" relations between magnitudes; we define e.g. "greater or equal" as "not-less than" (i.e.$a \ge b$ iff $\lnot a < b$) and we may use those "basic" relations to build up logical complex statement with "and", "or", "not" ... – Mauro ALLEGRANZA Apr 08 '14 at 09:55

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