Creating mathematical infinities: Metaphor, blending, and the beauty of transfinite cardinals

摘要: Abstract The infinite is one of the most intriguing, controversial, and elusive ideas in which human mind has ever engaged. In mathematics, a particularly interesting form infinity—actual infinity—has gained, over centuries, an extremely precise rich meaning, to point that it now lies at very core many fundamental fields such as calculus, fractal geometry, set theory. this article I focus on specific case actual infinity, namely, transfinite cardinals , conceived by imaginative controversial characters history 19th century mathematician Georg Cantor (1845–1918). analysis based Basic Metaphor Infinity (BMI). BMI everyday conceptual mechanism, originally outside hypothesized be responsible for creation all kinds mathematical infinities, from points infinity projective geometry sets, infinitesimal numbers, least upper bounds [Lakoff, George, Nunez, Rafael, 2000. Where Mathematics Comes From: How Embodied Mind Brings into Being. Books, New York]. analyze terms non-unidirectional mapping: double-scope blend. Under view “BMI” becomes Mapping Infinity.