Mind and Infinity

Abhijit Manohar^1,

¹Kolhapur, Maharashtra, India

Cite this paper:
Abhijit Manohar. Mind and Infinity. Applied Mathematics and Physics. 2021; 9(1):16-27. doi: 10.12691/amp-9-1-4

Abstract

The paper presents the general intuition of the concept of infinity. The Ramanujan’s Infinite series is reviewed in the light of proposed theory though the mathematical proof is presented more convincingly later in the article. The article discusses the cosmology and the size of universe and contrasts the finite vs. infinite universe arguments. The article questions and comments about the existence of transcendental numbers and Cantor’s Diagonal argument and also proves the problems with cardinality of infinity. It further gives other instantiations of intuitions and the consequences of mathematical infinity in limits, calculus, irrationals and series, respectively. The paper also suggests empirical methods for confirming the understanding of infinity presented in this paper in future. The 2 arguments – flexibility of mind (a priori intuition) and problem of the cardinality of infinity are presented and proved in this article. Both cognitive and mathematical explanation is provided to reinforce the idea that infinity is an a priori intuition without any physical counterpart.

Keywords:
infinity infinitesimal mind infinite series finite universe nothing intuitions brain calculus heuristics limits convergent and divergent series Ramanujan’s Summation cantor’s diagonal argument irrational numbers cardinality paradox

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