Sum–difference ratio

Sum–difference ratio is the mathematical operation in which to calculate the ratio of the sum and difference between the two given numbers. The operation sign is backward slash, \. The ratio increases when the difference between the two given number decreases as the following examples show.


 * 5\0 = (5+0)/(5−0) = 5/5 = 1
 * 5\1 = (5+1)/(5−1) = 6/4 = 1.5
 * 5\2 = (5+2)/(5−2) = 7/3 = 2.
 * 5\3 = (5+3)/(5−3) = 8/2 = 4
 * 5\4 = (5+4)/(5−4) = 9/1 = 9
 * 5\5 = (5+5)/(5−5) = 10/0 = ∞

The operation with the second given number being zero always result in the ratio of one as adding and subtracting zero always leaves the first given number and dividing two identical given numbers equals one. The operation with two of the same given numbers always result in infinity as subtracting two equal numbers equal zero and dividing any number by zero results in infinity.

As we continue the example from above as the second given number gets even higher, after reaching infinity in ratio, the ratio becomes negative and forever gets lower in degree approaching −1.

...
 * 5\6 = (5+6)/(5−6) = 11/−1 = −11
 * 5\7 = (5+7)/(5−7) = 12/−2 = −6
 * 5\8 = (5+8)/(5−8) = 13/−3 = −4.
 * 5\9 = (5+9)/(5−9) = 14/−4 = −3.5
 * 5\10 = (5+10)/(5−10) = 15/−5 = −3
 * 5\20 = (5+20)/(5−20) = 25/−15 = −1.
 * 5\50 = (5+50)/(5−50) = 55/−45 = −1.

Going in the other direction from the first example operation.


 * 5\−1 = (5+−1)/(5−−1) = 4/6 = 0.
 * 5\−2 = (5+−2)/(5−−2) = 3/7 = 0.
 * 5\−3 = (5+−3)/(5−−3) = 2/8 = 0.25
 * 5\−4 = (5+−4)/(5−−4) = 1/9 = 0.
 * 5\−5 = (5+−5)/(5−−5) = 0/10 = 0

The resulting ratio from the corresponding negative second given number is the multiplicative inverse of the corresponding positive second given number. Going beyond −5 as the second given number would get below zero and ever getting closer to −1.