Undergrad Does Defining ##g(y)## as ##h(y)^n## Validate the Statement?

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The discussion centers on the validity of defining the function ##g(y)## as ##h(y)^n## in mathematical logic. Participants assert that this definition lacks justification and does not support the statement in question. Specifically, the absence of a quantifier on ##h(y)## in the initial statement is highlighted as a critical flaw. The consensus is that while the definition may hold true, it does not provide any proof or substantial argumentation.

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What to say about this?
1659958487965.png

Is the logic used in the solution supports the statement?
 
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No. You just asserted that ##g(y)=h(y)^n## with no justification.
 
There is quite a bit of information missing. E.g., there is no quantifier on ##h(y)## in the initial statement.
 
TeethWhitener said:
No. You just asserted that ##g(y)=h(y)^n## with no justification.
IMG_20220808_182840.jpg
 
If you define ##g(y)## as ##h(y)^n##, then of course it's true, but there's also nothing to prove; it's all definitions.
 

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