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Dec 9 |
comment |
An algebra of “integrals”
Thanks! What if I just want this $T$ be defined on just a subspace? 1 is translational invariant, that certainly gives some trouble. ($\sin x$ seems to give similar trouble if one translate it by $\pi$.) |

Dec 8 |
awarded | Nice Question |

Dec 8 |
revised |
An algebra of “integrals”
clarified a bit. |

Dec 8 |
comment |
An algebra of “integrals”
I don't insist having something over $\mathbb{R}$. I just want to see if these kind of things may work. |

Dec 8 |
revised |
An algebra of “integrals”
added 17 characters in body; edited title |

Dec 8 |
revised |
An algebra of “integrals”
added 146 characters in body; edited tags |

Dec 7 |
comment |
Groups that do not exist
@Arturo, thanks for the correction, but I cannot edit the comment :(. |

Dec 7 |
comment |
Groups that do not exist
Great question. I wanted to ask something related, namely, what do we learn from those arguments that shows finite simple groups of a certain order does not exist? Those thing appear in abstract algebra course bothers beginners, and I'm not sure how useful they are for the training of a mathematician. (e.g. there cannot be a simple group of order 112, and it does not easily follow from Sylow theorems, but what's the point? (It does follow from the $p^aq^b$ theorem of Frobenius though.)) |