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At the End of Infinity
General Mathematics · Submitted 10 Mar 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim By developing its arithmetical properties for each basic operation, we'll show that infinity can be quantified with precision, and that no set, however large, is uncountable.
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The abstract, sentence by sentence
From 1873 to 1897, Georg Cantor worked on developing set theory, and despite a strong initial resistance, it rapidly became accepted as the foundation of mathematics. In this work, however, we'll demonstrate that Cantor's use of infinity is inconsistent with Calculus. Since both the cardinal and the ordinal numbers are to blame, we'll introduce the new infinite number $\lambda$ to remedy this situation. By developing its arithmetical properties for each basic operation, we'll show that infinity can be quantified with precision, and that no set, however large, is uncountable. Moreover, by working with the number $\lambda$, we'll resolve several long-standing paradoxes in mathematics, such as the Riemann Rearrangement Theorem and the Banach-Tarski paradox.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | From 1873 to 1897, Georg Cantor worked on developing set theory, and despite a strong initial resistance, it rapidly became accepted as the foundation of mathematics. | background 1.00 | 0.03 | 0.02 | asserted 1.00 |
| s1 | In this work, however, we'll demonstrate that Cantor's use of infinity is inconsistent with Calculus. | contribution 0.46 | 0.61 | 0.69 | asserted 1.00 |
| s2 | Since both the cardinal and the ordinal numbers are to blame, we'll introduce the new infinite number $\lambda$ to remedy this situation. | contribution 0.96 | 0.66 | 0.16 | asserted 0.99 |
| s3 | By developing its arithmetical properties for each basic operation, we'll show that infinity can be quantified with precision, and that no set, however large, is uncountable. | result 0.75 | 0.84 | 0.38 | asserted 1.00 |
| s4 | Moreover, by working with the number $\lambda$, we'll resolve several long-standing paradoxes in mathematics, such as the Riemann Rearrangement Theorem and the Banach-Tarski paradox. | result 0.77 | 0.73 | 0.19 | asserted 1.00 |
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Original abstract
From 1873 to 1897, Georg Cantor worked on developing set theory, and despite a strong initial resistance, it rapidly became accepted as the foundation of mathematics. In this work, however, we'll demonstrate that Cantor's use of infinity is inconsistent with Calculus. Since both the cardinal and the ordinal numbers are to blame, we'll introduce the new infinite number $\lambda$ to remedy this situation. By developing its arithmetical properties for each basic operation, we'll show that infinity can be quantified with precision, and that no set, however large, is uncountable. Moreover, by working with the number $\lambda$, we'll resolve several long-standing paradoxes in mathematics, such as the Riemann Rearrangement Theorem and the Banach-Tarski paradox.
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