Years ago in calculus class I excitedly learned that an infinite number of terms may have a finite sum. Manipulation of infinities seems somewhat routine to me now but my early ideas of calculus enlarged me a thousand-fold. Algebra was a language, geometry was a world-view, and calculus was a big idea. Like any big idea, even though it had been hundreds of years in formation, it met with resistance. In 1764 Bishop George Berkeley attacked the logical foundations of the calculus that Isaac Newton had unified. Here, from the online mathematics magazine plus, is a description of the attack.
Showing posts with label infinities. Show all posts
Showing posts with label infinities. Show all posts
Tuesday, September 14, 2010
Saturday, July 24, 2010
The infinitude of ecstacy -- a la Israel Lewis
Israel Lewis is the pen name of a polymath who earned his living as a scientist and is a writer in his retirement. His webpage offers a variety of his creations--many of them permeated with mathematics.
Labels:
Aleph Null,
ecstacy,
Georg Cantor,
infinite,
infinities,
infinitude,
Israel Lewis,
one,
transfinite,
zero
Tuesday, May 18, 2010
Glances at Infinity
Counter-intuitive notions are among my favorite parts of mathematics and, in considerations of infinity, these are numerous. Recalling Zeno's paradox, we capture the infinite finitely in this summation:
1 + 1/2 + 1/4 + 1/23 + . . . + 1/2n + . . . = 1
1 + 1/2 + 1/4 + 1/23 + . . . + 1/2n + . . . = 1
Labels:
Frank Dux,
infinities,
infinity,
Lillian R Lieber,
Lucille Lang Day,
mathematician,
mathematics,
poetry,
series,
sum,
Zeno
Monday, April 26, 2010
Poems starring mathematicians - 3
Today's poems illustrate the satirical humor and rhyme that frequently inhabit poems by mathematicians. (Previous postings of poems about mathematicians include March 23, April 14, and April 15.)
I Even Know of a Mathematician by John L Drost
“I even know of a mathematician who slept with his wife only
on prime-numbered days…” Graham said.
―Paul Hoffman, The Man Who Loved Only Numbers
I Even Know of a Mathematician by John L Drost
“I even know of a mathematician who slept with his wife only
on prime-numbered days…” Graham said.
―Paul Hoffman, The Man Who Loved Only Numbers
Labels:
continua,
decimal,
discrete,
infinities,
irrational,
John Drost,
Keith Allen Daniels,
mathematician,
numbers,
pi,
primes,
Rankine,
Sandburg,
transcendental
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