Is There a Real Solution for a^n+b^n=c^n as n Approaches Infinity?

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SUMMARY

The discussion centers on the equation an + bn = cn and the assertion that there are no real solutions for a, b, c as n approaches infinity. Participants argue that while real solutions exist for finite values of n, the concept of evaluating the equation at n = ∞ is mathematically meaningless. The consensus is that limits can be used to analyze the behavior of expressions as n increases, but cannot be applied to find solutions for equations at infinity.

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  • #61
matt grime said:
Both forms are not equivalent though because of that "limit" word in there (n is a dummy vairable, not actually a variable).

Yes, and this is the reason I had misgivings about solving equations with the limit notation in them. Certainly that works fine in special cases, as you illustrated.
 
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  • #62
this thread was so depressing from the beginning i never jumped in. questions need to be clearly stated before an answer is possible. the problem posed originally was never actually defined.

please stop this.
 
  • #63
If I could edit this, I would simply change "real" to "positive integer", and the problem would go away.
 

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