Mathematically Explain Non-defined Status of s=1

[electronic engineer]

let's assume such equation:

s=1+(y/x)

we usually say that s=1 when both x,y has Zero value

how to explain that mathematically?!

 

[daveb]

no, we can't say x and y are 0, but we must stipulte y/x = 0. If y and x both = zero, then the value s is undefined since y/x is undefined. And if y/x = 0, then y=0, and x is not equal to 0.

 

[HallsofIvy]

let's assume such equation:

s=1+(y/x)

we usually say that s=1 when both x,y has Zero value

how to explain that mathematically?!

I can't explain it because I would never say such a thing! If you approach (0,0) along the line y= x, then s will have a limit of 2. If you approach along the line y= -x, then s will have limit of 0. In fact, given any value a, then approaching (0,0) along the line y= (a-1)x, s has limit a.