...
  • 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Advances in Pure Mathematics >Apropos 1+2+3+4+5+...=: Mapping Infinity in Light of the Number Circle (or Cycle), in L. Euler’s Footsteps and with the Aid of Two Dimensional Infinite Series, and Replacing Negative Infinity and Positive Infinity with Just Infinity
【24h】

Apropos 1+2+3+4+5+...=: Mapping Infinity in Light of the Number Circle (or Cycle), in L. Euler’s Footsteps and with the Aid of Two Dimensional Infinite Series, and Replacing Negative Infinity and Positive Infinity with Just Infinity

机译：Apropos 1 + 2 + 3 + 4 + 5 + ... =：根据L. Euler的脚步并借助二维无限级数，根据数圈（或周期）映射无穷大，并替换负无穷大和正无穷大无限无限

获取原文
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

The number circle—that is, the notion that the largest possible positive numbers are followed by infinity and then by the smallest possible negative numbers—is not new. L. Euler defended it in the eighteenth century and, before him, J. Wallis considered something vaguely similar. However, in the nineteenth century, the number circle was for the most part abandoned—even if something similar is on occasion accepted in geometry, in the sense that space is circular. The design of the present paper is to present positive proof of the veracity of the number circle and therefore, at the same time, to falsify the number line. Verifying the number circle implies falsifying negative infinity and positive infinity—infinity instead being neither negative nor positive, just like 0. Part of said proof involves showing that infinity can be defined both as 1+1+1+1+1+1+... and as -1-1-1-1-1-... and that the following Equation applies: 1+1+1+1+1+1+...=-1-1-1-1-1-... The principal mathematical technique that will be used to provide said proof is introduced here for the first time. It is called the two dimensional infinite series. It is an infinite series of infinite series. Some additional observations regarding the geography of infinity will be made. A more detailed description of the geography of infinity will be reserved for other papers. The Equation is discussed in this paper only to the extent that the attention that has been paid to it has necessitated the construction of a theory of infinity that, upon closer inspection, makes the Equation more self-evident and intuitively apparent; a fuller discussion will take place in a later paper.
机译：数字圈（即，最大可能的正数后跟无穷大，然后最小的可能的负数的概念）并不是什么新鲜事物。欧拉（L. Euler）在18世纪为它辩护，在他之前，沃利斯（J. Wallis）认为有些模糊的相似之处。但是，在19世纪，数字圆在很大程度上被放弃了-即使有时几何学上也接受了类似的东西，即空间是圆形的。本文的设计是对数字圆的真实性提出积极的证明，因此，同时要伪造数字线。验证数字圈意味着伪造负无穷大和正无穷大-就像0一样，无穷大既不是负也不是正。就像是证明，部分证明包括表明无穷大可以定义为1 + 1 + 1 + 1 + 1 + 1 +。 ..和-1-1-1-1-1 -...，并适用以下公式：1 + 1 + 1 + 1 + 1 + 1 + 1 + ... =-1-1-1-1- 1 -...这里将首次介绍将用于提供所述证明的主要数学技术。它称为二维无限级数。它是无限级数的无限级数。关于无穷远的地理学，还将进行一些其他观察。无限地理的更详细描述将保留给其他论文。本文仅在以下程度上讨论了该方程，即，已经引起了对方程的关注，因此有必要构建无穷大理论，在进行更仔细的检查后，该定理将变得更加不言而喻并且直观直观。稍后的论文中将进行更充分的讨论。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号