
E. Rocha replied to the topic RRR in the forum 40xx Sequences, series, summability 2 years ago
[latex]
[+preamble]
newtheorem{dfn}{Definition}
newtheorem{theo}{Theorem}
newtheorem{prob}{Problem}
newtheorem{prop}[theo]{Proposition}
newtheorem{lmm}[theo]{Lemma}
newtheorem{clm}{Claim}
newtheorem{rmk}{Remark}
newtheorem{claim}{Claim}
newenvironment{proof}{textit{Proof.} small}{normalsize…[Read more] 
E. Rocha replied to the topic RRR in the forum 40xx Sequences, series, summability 2 years ago
[latex]
[+preamble]
newcommand{cf}{mbox{cf}}
newcommand{ls}{left<}
newcommand{rs}{right>}
newcommand{RS}{mathcal{RS}}
newcommand{cfn}[3]{left{#2::#3right}_{#1}}
[/preamble]
section*{Operations}The textbf{aggregation operation} $varphi_{m,q}:mathcal{RS}rightarrowmathcal{RS}$
with $m,qinbkNz$ and $q<m$, is the map such that,
$$ w =…[Read more] 
E. Rocha replied to the topic RRR in the forum 40xx Sequences, series, summability 2 years ago
[latex]
[+preamble]
newcommand{cf}{mbox{cf}}
newcommand{ls}{left<}
newcommand{rs}{right>}
newcommand{RS}{mathcal{RS}}
newcommand{cfn}[3]{left{#2::#3right}_{#1}}
[/preamble]
section*{Operations}The textbf{aggregation operation} $varphi_{m,q}:mathcal{RS}rightarrowmathcal{RS}$,
with $m,qinbkNz$ and $q<m$, is the map such that,
$$ w =…[Read more] 
E. Rocha replied to the topic RRR in the forum 40xx Sequences, series, summability 2 years ago
[+preamble]
newcommand{cf}{mbox{cf}}
newcommand{ls}{left<}
newcommand{rs}{right>}
newcommand{RS}{mathcal{RS}}
newcommand{cfn}[3]{left{#2::#3right}_{#1}}
[/preamble]
section*{Operations}The textbf{aggregation operation} $varphi_{m,q}:mathcal{RS}rightarrowmathcal{RS}$,
with $m,qinbkNz$ and $q<m$, is the map such that,
$$ w =…[Read more] 
E. Rocha replied to the topic RRR in the forum 40xx Sequences, series, summability 2 years ago
[+preamble]
newcommand{cf}{mbox{cf}}
newcommand{ls}{left<}
newcommand{rs}{right>}
newcommand{RS}{mathcal{RS}}
newcommand{cfn}[3]{left{#2::#3right}_{#1}}
[/preamble]$
section*{Operations}The textbf{aggregation operation} $varphi_{m,q}:RSrightarrowRS$,
with $m,qinbkNz$ and $q<m$, is the map such that,
$$ w = varphi_{m,q}(u):::mbox{ and }::: w_i…[Read more] 
E. Rocha replied to the topic RRR in the forum 40xx Sequences, series, summability 2 years ago
[+preamble]
newcommand{cf}{mbox{cf}}
newcommand{ls}{left<}
newcommand{rs}{right>}
newcommand{RS}{mathcal{RS}}
newcommand{cfn}[3]{left{#2::#3right}_{#1}}
[/preamble]$
section*{Operations}The textbf{aggregation operation} $varphi_{m,q}:RSrightarrowRS$,
with $m,qinbkNz$ and $q<m$, is the map such that,
$$ w = varphi_{m,q}(u):::mbox{ and }::: w_i…[Read more] 
E. Rocha replied to the topic RRR in the forum 40xx Sequences, series, summability 2 years ago
[latex]
[+preamble]
newtheorem{dfn}{Definition}
newtheorem{theo}{Theorem}
newtheorem{prob}{Problem}
newtheorem{prop}[theo]{Proposition}
newtheorem{lmm}[theo]{Lemma}
newtheorem{clm}{Claim}
newtheorem{rmk}{Remark}
newtheorem{claim}{Claim}
newenvironment{proof}{textit{Proof.} small}{normalsize…[Read more] 
E. Rocha replied to the topic RRR in the forum 40xx Sequences, series, summability 2 years ago
[latexpage]
[+preamble]
newtheorem{dfn}{Definition}
newtheorem{theo}{Theorem}
newtheorem{prob}{Problem}
newtheorem{prop}[theo]{Proposition}
newtheorem{lmm}[theo]{Lemma}
newtheorem{clm}{Claim}
newtheorem{rmk}{Remark}
newtheorem{claim}{Claim}
newenvironment{proof}{textit{Proof.} small}{normalsize…[Read more] 
E. Rocha replied to the topic RRR in the forum 40xx Sequences, series, summability 2 years ago
[latexpage]
[+preamble]
newtheorem{dfn}{Definition}
newtheorem{theo}{Theorem}
newtheorem{prob}{Problem}
newtheorem{prop}[theo]{Proposition}
newtheorem{lmm}[theo]{Lemma}
newtheorem{clm}{Claim}
newtheorem{rmk}{Remark}
newtheorem{claim}{Claim}
newenvironment{proof}{textit{Proof.} small}{normalsize…[Read more] 
E. Rocha replied to the topic RRR in the forum 40xx Sequences, series, summability 2 years ago
$
[+preamble]
newtheorem{dfn}{Definition}
newtheorem{theo}{Theorem}
newtheorem{prob}{Problem}
newtheorem{prop}[theo]{Proposition}
newtheorem{lmm}[theo]{Lemma}
newtheorem{clm}{Claim}
newtheorem{rmk}{Remark}
newtheorem{claim}{Claim}
newenvironment{proof}{textit{Proof.} small}{normalsize…[Read more] 
E. Rocha replied to the topic RRR in the forum 40xx Sequences, series, summability 2 years ago
[latex]
[+preamble]
newtheorem{dfn}{Definition}
newtheorem{theo}{Theorem}
newtheorem{prob}{Problem}
newtheorem{prop}[theo]{Proposition}
newtheorem{lmm}[theo]{Lemma}
newtheorem{clm}{Claim}
newtheorem{rmk}{Remark}
newtheorem{claim}{Claim}
newenvironment{proof}{textit{Proof.} small}{normalsize…[Read more] 
E. Rocha replied to the topic RRR in the forum 40xx Sequences, series, summability 2 years ago
[latex]
[+preamble]
newtheorem{dfn}{Definition}
newtheorem{theo}{Theorem}
newtheorem{prob}{Problem}
newtheorem{prop}[theo]{Proposition}
newtheorem{lmm}[theo]{Lemma}
newtheorem{clm}{Claim}
newtheorem{rmk}{Remark}
newtheorem{claim}{Claim}
newenvironment{proof}{textit{Proof.} small}{normalsize…[Read more] 
E. Rocha replied to the topic RRR in the forum 40xx Sequences, series, summability 2 years ago
[latex]
[+preamble]
newtheorem{dfn}{Definition}
newtheorem{theo}{Theorem}
newtheorem{prob}{Problem}
newtheorem{prop}[theo]{Proposition}
newtheorem{lmm}[theo]{Lemma}
newtheorem{clm}{Claim}
newtheorem{rmk}{Remark}
newtheorem{claim}{Claim}
newenvironment{proof}{textit{Proof.} small}{normalsize…[Read more] 
E. Rocha started the topic Regular aggregation sequences and their (in)finite series in the forum 40xx Sequences, series, summability 2 years ago
Motivated by the (renormalization) of some classical divergent series in String Theory, e.g.
[math] sum_{n=1}^{+infty} n = frac{1}{12}
::mbox{ (yes, it means) } 1 + 2+ 3+ 4+5+6+dots = frac{1}{12}[/math](see here), I start thinking on the convergence meaning of a class of divergent series, trying to make sense of them without following some of…[Read more]

E. Rocha started the topic Regular aggregation sequences and their (in)finite series in the forum 40xx Sequences, series, summability 2 years ago
Motivated by the (renormalization) of some classical divergent series in String Theory, e.g.
[math] sum_{n=1}^{+infty} n = frac{1}{12}
::mbox{ (yes, it means) } 1 + 2+ 3+ 4+5+6+dots = frac{1}{12}[/math](see here), I start thinking on the convergence meaning of a class of divergent series, trying to make sense of them without following…[Read more]

E. Rocha started the topic Regular aggregation sequences and their (in)finite series in the forum 40xx Sequences, series, summability 2 years ago
Motivated by the (renormalization) of some classical divergent series in String Theory, e.g.
[math] sum_{n=1}^{+infty} n = frac{1}{12}
::mbox{ (yes, it means) } 1 + 2+ 3+ 4+5+6+dots = frac{1}{12}[/math](see here), I start thinking on the convergence meaning of a class of divergent series, trying to make sense of them without following…[Read more]

E. Rocha started the topic Regular aggregation sequences and their (in)finite series in the forum 40xx Sequences, series, summability 2 years ago
Motivated by the (renormalization) of some classical divergent series in String Theory, e.g.
[math] sum_{n=1}^{+infty} n = frac{1}{12}
::mbox{ (yes, it means) } 1 + 2+ 3+ 4+5+6+dots = frac{1}{12}[/math](see here), I start thinking on the convergence meaning of a class of divergent series, trying to make sense of them without following…[Read more]

E. Rocha started the topic Regular aggregation sequences and their (in)finite series in the forum 40xx Sequences, series, summability 2 years ago
Motivated by the (renormalization) of some classical divergent series in String Theory, e.g.
[math] sum_{n=1}^{+infty} n = frac{1}{12}
::mbox{ (yes, it means) } 1 + 2+ 3+ 4+5+6+dots = frac{1}{12}[/math](see here), I start thinking on the convergence meaning of a class of divergent series, trying to make sense of them without following…[Read more]

E. Rocha started the topic Regular aggregation sequences and their (in)finite series in the forum 40xx Sequences, series, summability 2 years ago
Motivated by the (renormalization) of some classical divergent series in String Theory, e.g.
$$ sum_{n=1}^{+infty} n = frac{1}{12}
::mbox{ (yes, it means) } 1 + 2+ 3+ 4+5+6+dots = frac{1}{12}$$(see here), I start thinking on the convergence meaning of a class of divergent series, trying to make sense of them without following some of the…[Read more]

E. Rocha started the topic RRR in the forum 40xx Sequences, series, summability 2 years ago
Motivated by the (renormalization) of some classical divergent series in String Theory, e.g.
$$ sum_{n=1}^{+infty} n = frac{1}{12}
::mbox{ (yes, it means) } 1 + 2+ 3+ 4+5+6+dots = frac{1}{12}$$(see here), I start thinking on the convergence meaning of a class of divergent series, trying to make sense of them without following some of the…[Read more]
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