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

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Discussion Overview

The discussion revolves around the validity of defining the function ##g(y)## as ##h(y)^n## and whether this definition supports a particular statement. The scope includes logical reasoning and the implications of definitions in mathematical contexts.

Discussion Character

  • Debate/contested

Main Points Raised

  • Some participants question the justification for asserting that ##g(y)=h(y)^n##, indicating a lack of supporting logic.
  • Others note that the initial statement lacks a quantifier on ##h(y)##, suggesting that important information is missing.
  • One participant argues that defining ##g(y)## as ##h(y)^n## makes the statement trivially true, but emphasizes that this is merely a matter of definitions without further proof required.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there are competing views regarding the justification and implications of the definition.

Contextual Notes

Limitations include the absence of a quantifier on ##h(y)## and the reliance on definitions without further exploration of their implications.

Vibhukanishk
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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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