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3. Show that all (total) functions on the non-negative integers a assuming values in w are not countably infinite.

3. Show that all (total) functions on the non-negative integers a assuming values in w are not countably infinite.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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3. Show that all (total) functions on the non-negative integers w assuming values in w are not countably infinite. 4. Give an informal argument for establishing that all total computable functions are countably infinite. Conclude that not all functions (in the mathematical sense) on w taking values in w are computable functions. (We will later come across concrete examples of non-computable functions.)
Transcribed Image Text:3. Show that all (total) functions on the non-negative integers w assuming values in w are not countably infinite. 4. Give an informal argument for establishing that all total computable functions are countably infinite. Conclude that not all functions (in the mathematical sense) on w taking values in w are computable functions. (We will later come across concrete examples of non-computable functions.)
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