Is (nearly) all mathematics addition?

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    Addition Mathematics
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Discussion Overview

The discussion revolves around the proposition that nearly all mathematics can be reduced to addition. Participants explore various mathematical concepts, including arithmetic, logarithmic functions, derivatives, and functions in different mathematical domains, questioning the validity of the original claim and examining the implications of such a reductionist view.

Discussion Character

  • Debate/contested
  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that all mathematical operations can be expressed in terms of addition, providing examples such as subtraction as addition of negative numbers and multiplication as repeated addition.
  • Another participant counters that the reduction to addition is limited to arithmetic and does not encompass broader mathematical concepts like logarithmic functions.
  • Some participants argue that multiplication cannot be universally expressed as addition, particularly for non-integer values.
  • There is a discussion about the complexity of evaluating functions like e^(iπ) and the tediousness of using Taylor series expansions to express trigonometric functions in terms of addition.
  • Participants raise the challenge of simplifying concepts from topology and abstract algebra to addition, questioning the validity of the original hypothesis.
  • One participant acknowledges the flaws in their hypothesis and emphasizes that they did not intend to claim that all mathematics can be reduced to addition.
  • Another participant discusses the foundational aspects of set theory and how basic notions can relate to addition.
  • There are mentions of various mathematical fields, such as geometry and game theory, that may not be reducible to addition.
  • Some participants explore the relationship between addition and computer science, discussing how computers fundamentally rely on addition in their operations.
  • Others argue that computers can be based on logic gates and other operations that do not necessarily involve addition.

Areas of Agreement / Disagreement

Participants do not reach a consensus. There are multiple competing views regarding the extent to which mathematics can be reduced to addition, with some arguing against the hypothesis and others acknowledging its limitations while still exploring its implications.

Contextual Notes

Participants express uncertainty about the applicability of the reductionist view across different mathematical domains, highlighting limitations in definitions and the complexity of certain mathematical concepts.

  • #31
cmcraes said:
Division: 1/Multiplication
You are saying, Division : Division.
How does that save you from doing division?
 
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  • #32
phinds said:
How about these? Do you reckon they reduce to addition?

geometry
topology
abstract algebra
prepositional logic
Fourier analysis
Laplace transforms
differential equations
set theory
game theory

and those are just ones that come to mind and I don't know all that much about math even at the undergraduate level. I'm sure there are lots I'm leaving off that really have little or nothing to do with addition. Your hypothesis is seriously flawed.

Wow, I'm not sure who pissed in your cheerios but I'm pretty sure it wasn't the OP.
 

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