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Additive function, continuity in R

发表于 2010-10-4 23:43 | 显示全部楼层 |阅读模式

I';ve worked out the first 3.
The last question is quite a leap, from Q to R.

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发表于 2010-10-5 00:37 | 显示全部楼层

Additive function, continuity in R

Just pick a sequence {r(n)} of rationals that tends to x. By the continuity of f, you are done.

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楼主| 发表于 2010-10-5 01:08 | 显示全部楼层

Additive function, continuity in R

Continuity of f has not been proven.

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发表于 2010-10-5 01:54 | 显示全部楼层

Additive function, continuity in R

If not assume continuity, the conclusion is not right.

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楼主| 发表于 2010-10-5 16:33 | 显示全部楼层

Additive function, continuity in R

Alright, I see.

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