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

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The discussion centers on the validity of defining g(y) as h(y)^n in relation to a specific statement. Participants argue that the logic supporting this definition lacks justification and is insufficiently detailed. The absence of a quantifier on h(y) is highlighted as a critical omission. It is emphasized that while defining g(y) in this manner makes the statement trivially true, it does not constitute a proof. Overall, the consensus is that the assertion does not validate the statement due to its reliance on definitions rather than logical reasoning.
Vibhukanishk
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What to say about this?
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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.
 
First trick I learned this one a long time ago and have used it to entertain and amuse young kids. Ask your friend to write down a three-digit number without showing it to you. Then ask him or her to rearrange the digits to form a new three-digit number. After that, write whichever is the larger number above the other number, and then subtract the smaller from the larger, making sure that you don't see any of the numbers. Then ask the young "victim" to tell you any two of the digits of the...

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