- #1
sgfw
- 15
- 0
From what I can tell, it seems that 1/x + δ(x) = 1/x because if we think of both 1/x and the dirac delta function as the following peicewise functions:
1/x = 1/x for x < 0
1/x = undefined for x = 0
1/x = 1/x for x > 0
δ(x) = 0 for x < 0
δ(x) = undefined for x = 0
δ(x) = 0 for x > 0
then for any part of 1/x that is defined, 0 is being added to it. Is it okay to ignore the fact that the function is being changed at x = 0 because it was already undefined?
1/x = 1/x for x < 0
1/x = undefined for x = 0
1/x = 1/x for x > 0
δ(x) = 0 for x < 0
δ(x) = undefined for x = 0
δ(x) = 0 for x > 0
then for any part of 1/x that is defined, 0 is being added to it. Is it okay to ignore the fact that the function is being changed at x = 0 because it was already undefined?