[分析] f(x)+f(y)=f(x+y) for all x,y in R.

[gg (GG)]

f: R-> R
f(x)+f(y)=f(x+y) for all x,y in R

If f is continuous at some p in R, it follows that f is continuous on R.
Then we can conclude that f(x)=cx for all x in R, where c is a constant.

How about the condition that f(x) is discontinuous at each point x of R?
If possible, please construct an explicit example.

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推 zombiea     :consider R as Q-vector space with basis {x}
→ zombiea     :and chose {x} contained in [0,1]
→ zombiea     :then regard R->R as Q linear transform by
→ zombiea     :x->1 for all basis x , then this is what you need
推 cacud       :好像泛函的題目@@
推 THEJOY      :#18YhYIfr 或 搜尋作者THEJOY第二篇