Does there exist a set of all functions? Suppose such a set exists and call it F. Define a "function" F from to {0,1} as follows: = -{o otherwise the domain off and ƒ(ƒ) = 0, 0 F(f): Show using an argument similar to the Russell's paradox that this leads to a contra- diction.
Does there exist a set of all functions? Suppose such a set exists and call it F. Define a "function" F from to {0,1} as follows: = -{o otherwise the domain off and ƒ(ƒ) = 0, 0 F(f): Show using an argument similar to the Russell's paradox that this leads to a contra- diction.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Does there exist a set of all functions? Suppose such a set exists and
call it F. Define a "function" F from F to {0,1} as follows:
F(f) = { if f is in the domain of ƒ and ƒ(ƒ) = 0,
0 otherwise.
Show using an argument similar to the Russell's paradox that this leads to a contra-
diction.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71fce221-a019-4b79-975b-72a989b78f32%2F0c11e43c-442a-473b-a7cd-493432bc49bc%2Fxn0em8_processed.png&w=3840&q=75)
Transcribed Image Text:Does there exist a set of all functions? Suppose such a set exists and
call it F. Define a "function" F from F to {0,1} as follows:
F(f) = { if f is in the domain of ƒ and ƒ(ƒ) = 0,
0 otherwise.
Show using an argument similar to the Russell's paradox that this leads to a contra-
diction.
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