Time Travel, Quantum Entanglement and Quantum Computing

Not only is the Universe stranger than we think, it is stranger than we can think…Hiesenberg

Archives for June, 2024 - Page 2

An accurate map of California is spread out flat on a table in Evans Hall, in Berkeley. Prove that there is exactly one point on the map lying directly over the point it represents.

June 13, 2024 An accurate map of California is spread out flat on a table in Evans Hall, in Berkeley. Prove that there is exactly one point on the map lying directly over the point it represents.2024-06-13T03:53:26+00:00 Pure Math
To prove that there is exactly one point on the map of California that lies directly over the point it represents, we can use a combination of the Brouwer Fixed-Point…
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Let f : R + R be continuous, with 00 s_, If(x)l dx < o. Show that there is a sequence (x,,) such that x, -+ 00, x, f (x,) 4 0, and x, f(-xc,) 4 0 as n -+ o.

June 12, 2024 Let f : R + R be continuous, with 00 s_, If(x)l dx < o. Show that there is a sequence (x,,) such that x, -+ 00, x, f (x,) 4 0, and x, f(-xc,) 4 0 as n -+ o.2024-09-09T18:29:54+00:00 Pure Math
Let f : R + R be continuous, with 00 s_, If(x)l dx < o. Show that there is a sequence (x,,) such that x, -+ 00, x, f (x,)…
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Given conditions: lim ⁑ 𝑑 β†’ π‘Ž 𝑔 ( 𝑑 ) = 𝑏 lim tβ†’a ​ g(t)=b lim ⁑ π‘₯ β†’ 𝑏 𝑓 ( π‘₯ ) = 𝑐 lim xβ†’b ​ f(x)=c To prove: lim ⁑ 𝑑 β†’ π‘Ž 𝑓 ( 𝑔 ( 𝑑 ) ) = 𝑐 lim tβ†’a ​ f(g(t))=c

June 12, 2024 Given conditions: lim ⁑ 𝑑 β†’ π‘Ž 𝑔 ( 𝑑 ) = 𝑏 lim tβ†’a ​ g(t)=b lim ⁑ π‘₯ β†’ 𝑏 𝑓 ( π‘₯ ) = 𝑐 lim xβ†’b ​ f(x)=c To prove: lim ⁑ 𝑑 β†’ π‘Ž 𝑓 ( 𝑔 ( 𝑑 ) ) = 𝑐 lim tβ†’a ​ f(g(t))=c2024-09-09T18:30:00+00:00 Pure Math
Given conditions: lim⁑tβ†’ag(t)=b\lim_{t \to a} g(t) = blimtβ†’a​g(t)=b lim⁑xβ†’bf(x)=c\lim_{x \to b} f(x) = climxβ†’b​f(x)=c To prove: lim⁑tβ†’af(g(t))=c\lim_{t \to a} f(g(t)) = climtβ†’a​f(g(t))=c Using the definition of the limit: lim⁑tβ†’ag(t)=b\lim_{t \to…
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