2 апр. 2012 г. · Ask Question. Viewed 4k times. 5. Linear functions are said to be additive: f(x+y)=f(x)+f(y) But if I have this simple function f(x)=7x+3, I ...

26 сент. 2013 г. · Let f be an additive function. So for all x,y∈R, f(x+y)=f(x)+f(y). if necessary the proofs should involve the δ−ε definition of a limit.

9 дек. 2017 г. · We have f:R→R and we know that f is both additive: f(x+y)=f(x)+f(y) and multiplicative: f(xy)=f(x)f(y) and I found out that this means that f(x) ...

31 июл. 2017 г. · A function T:V→W is additive if T(x+y)=T(x)+T(y) for every x,y∈V. If V and W are vector spaces over the field of Q, then show that every ...

31 июл. 2017 г. · A function T:V→W is additive if T(x+y)=T(x)+T(y) for every x,y∈V. Prove that there exists an additive function T:R→R that is not linear.

1 янв. 2021 г. · It is known that if every set of reals is measurable, then every additive function is linear. Is the converse true in ZF?

24 дек. 2011 г. · Proving that an additive function f is continuous if it is continuous at a single point ... Suppose that f is continuous at x0 and f satisfies f(x) ...

1 июн. 2012 г. · Problem: Let f(x):R→R be a continuous function satisfying f(x+y)=f(x)+f(y) for all x,y∈R. Show f is a linear transformation.

25 нояб. 2012 г. · If an additive function a(x) with the property that a(xy)=a(x)+a(y), when gcd(x,y)=1, then is a(1)=0, I think it should be, otherwise I would ...

6 февр. 2017 г. · If f is defined over the complex numbers, f:C⟶C, then finding a mapping which is additive but not homogenous is simple; for example, f(c)=c∗.