I know every continuous function from [0,1] to [0,1] has fixed point. I proved it using Intermediate value theorem. But I can not see why every continuous function from [0,1] to R has fixed point. Is this result even true?

Eliza Gregory

Eliza Gregory

Answered question

2022-10-20

I know every continuous function from [ 0 , 1 ] to [ 0 , 1 ] has fixed point. I proved it using Intermediate value theorem. But I can not see why every continuous function from [ 0 , 1 ] to R has fixed point.
Is this result even true?

Answer & Explanation

Krystal Dillon

Krystal Dillon

Beginner2022-10-21Added 10 answers

No. f ( x ) = x + 1 is a continuous function from [ 0 , 1 ] to R .

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