Proof of existence of real exponentiation

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I'm reading Tao's Analysis, and confused about this lemma



  1. Why the sequence $x^frac1k_k=1^infty$ is eventually $varepsilon x^-M$ close to 1?


  2. Why need to show the bound is the same when $n, m > N$ and $q_n leq q_m$ by symmetry?


Thanks!
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calculus proof-explanation




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  • In latex, and are grouping symbols; if you want to actually display them you need to escape them: write and respectively.
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up vote
1
down vote

favorite












I'm reading Tao's Analysis, and confused about this lemma



  1. Why the sequence $x^frac1k_k=1^infty$ is eventually $varepsilon x^-M$ close to 1?


  2. Why need to show the bound is the same when $n, m > N$ and $q_n leq q_m$ by symmetry?


Thanks!
enter image description here



enter image description here




calculus proof-explanation




share|cite|improve this question





















  • In latex, and are grouping symbols; if you want to actually display them you need to escape them: write and respectively.
    – Hurkyl
    Aug 1 at 16:58












up vote
1
down vote

favorite









up vote
1
down vote

favorite











I'm reading Tao's Analysis, and confused about this lemma



  1. Why the sequence $x^frac1k_k=1^infty$ is eventually $varepsilon x^-M$ close to 1?


  2. Why need to show the bound is the same when $n, m > N$ and $q_n leq q_m$ by symmetry?


Thanks!
enter image description here



enter image description here




calculus proof-explanation




share|cite|improve this question













I'm reading Tao's Analysis, and confused about this lemma



  1. Why the sequence $x^frac1k_k=1^infty$ is eventually $varepsilon x^-M$ close to 1?


  2. Why need to show the bound is the same when $n, m > N$ and $q_n leq q_m$ by symmetry?


Thanks!
enter image description here



enter image description here





calculus proof-explanation





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Aug 2 at 1:07









amWhy

189k25219431




189k25219431









asked Aug 1 at 16:50









Cathy

1067




1067











  • In latex, and are grouping symbols; if you want to actually display them you need to escape them: write and respectively.
    – Hurkyl
    Aug 1 at 16:58
















  • In latex, and are grouping symbols; if you want to actually display them you need to escape them: write and respectively.
    – Hurkyl
    Aug 1 at 16:58















In latex, and are grouping symbols; if you want to actually display them you need to escape them: write and respectively.
– Hurkyl
Aug 1 at 16:58




In latex, and are grouping symbols; if you want to actually display them you need to escape them: write and respectively.
– Hurkyl
Aug 1 at 16:58















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