Jack M
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 13h comment a question about rational power irrational is irrational? According to MathWorld this is an open problem. 14h comment a question about rational power irrational is irrational? @Asterrovels If $a$ is irrational then $2^a$ can be rational. In fact, for most rationals $x$, $\log_2(x)$ is an irrational number. For instance, you can easily prove by contradiction that $\log_2(3)$ is irrational, since if it wasn't you'd end up with a power of two being equal to a power of three. 20h comment a question about rational power irrational is irrational? @Asterrovels Okay, but in that case, since $a$ is irrational you can no longer claim that $(2^a)^{\frac 1 b}$ is irrational. 20h comment a question about rational power irrational is irrational? When you say "now assuming that $\log_2 p = \frac a b$", this is tantamount to saying, "let's assume $e$ is rational". 1d awarded Yearling 1d answered Please Explain Kuratowski Definition of Ordered Pairs May 1 comment Refuting the Anti-Cantor Cranks @DaveL.Renfro That in't a proof by contradiction, it's a proof by contrapositive. "If I am the murderer, then I was not at the party", to which the contrapositive is "If I was at the party, I am not the murderer." But even in mathematics, contradiction is often confused with contrapositive. Apr 30 asked Does the PNT establish a connection between primes and the logarithm? Apr 29 comment Number of points of accumulation of a sequence There's a classic theorem that if you walk around a circle in discrete steps of $a$ radians, where $a/\pi$ is irrational, then the set of points that you visit is dense in the circle. This implies that $(\sin(an))_{n\in\mathbb N}$ is dense in $[-1, 1]$, and you can take $a=1$ for a cute example of a sequence with infinitely many accumulation points. Apr 29 answered Prove that the Gaussian Integer's ring is a Euclidean domain Apr 29 comment Irrational numbers generated by a deterministic cellular automaton? I'm not sure why you're so pessimistic about proving that a cellular automata-generated number is transcendental, when you then immediately cite a very similar (and marvelous) result about how finite automata-generated numbers are transcendental. Apr 27 awarded Nice Answer Apr 24 comment Is there a way to write an infinite set that contains only irrational numbers without integer multiples? More generally, you're relying on the lemma that for any finite set of irrationals, the set of the their integer multiples does not cover the set of irrationals. But this is obvious: the set of integer multiples of any finite set is discrete, but the irrationals are dense. Apr 21 comment Injective: In what circumstances would there be less than one pre-image of an image? No, no - of course an "image with less than one (ie, zero) pre-image" is a contradiction, that can never happen. An injective function has no more than one pre-image for each image, but the opposite of "no more than one" isn't "less than one", it's "only one". Apr 20 answered why is $\sum\limits_{k=1}^{n} k^m$ a polynomial with degree $m+1$ in $n$ Apr 17 comment Is PA the first axiomatization of arithmetic to be discovered? Euclid sort of axiomatized arithmetic, or tried to. Apr 14 comment Does this equation my professor wrote actually work? @hexomino No no, that's not the problem - $(\frac 1 e)^0$ is well-defined. The problem is that for some reason the OP thinks $(\frac 1 e)^0$ should give $0.5$, which it shouldn't - $0.9$ (ish) is correct. How do you figure that's 0.5, OP? Apr 13 awarded elementary-number-theory Apr 12 comment How Are The Graphs Related? @JebusCrust Then it moves to the left by $c$ units. Apr 12 answered Concise proof that every common divisor divides GCD without Bezout's identity?