Discover Other Solutions to 1+1=2 | Newbie's Guide to Math Equations"

  • Context: High School 
  • Thread starter Thread starter asdfghjklqqww
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around the question of whether there are alternative answers to the equation 1+1=2, exploring various mathematical structures and interpretations. Participants consider different algebraic systems, representations, and contexts in which the equation might yield different results.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • Some participants inquire if there are cases where 1+1 equals something other than 2.
  • One participant mentions that in complex numbers, the only answer is 2, but notes that 1.9999... is another representation.
  • Another participant introduces the ring Z_2, where 1+1=0, suggesting that in this structure, 2 is equivalent to 0.
  • There are claims that in binary representation, 1+1 equals 10.
  • Some participants argue that alternate solutions to 1+1=2 often involve breaking mathematical rules or manipulating equations incorrectly.
  • Discussion includes references to historical proofs of 1+1=2, with some confusion about authorship, attributing it to Bertrand Russell and Alfred North Whitehead rather than Newton.
  • Participants express curiosity about the need for rigorous proofs of seemingly obvious statements like 1+1=2.
  • There is mention of vector addition, where the result of adding two vectors can yield values between 0 and 2, depending on their orientation.

Areas of Agreement / Disagreement

Participants generally agree that in standard arithmetic, 1+1=2, but multiple competing views exist regarding alternative mathematical contexts and interpretations. The discussion remains unresolved regarding the validity and implications of these alternative interpretations.

Contextual Notes

Some statements rely on specific definitions of mathematical operations and structures, which may not be universally accepted. The discussion touches on various algebraic systems and their rules, highlighting the complexity of the topic.

Who May Find This Useful

This discussion may be of interest to those exploring foundational mathematics, algebraic structures, or the philosophy of mathematics.

  • #31
one plus one equals three if


one equals 1.5
 
Mathematics news on Phys.org
  • #32
asdfghjklqqww said:
one plus one equals three if


one equals 1.5

...yes, iff 1=1.5, then 1+1=3. However, 1\neq1.5, so therefore 1+1\neq3.
 
  • #33
Char. Limit said:
...yes, iff 1=1.5, then 1+1=3. However, 1\neq1.5, so therefore 1+1\neq3.
While true, this is an invalid argument. Fallacy of the inverse or something like that.
 

Similar threads

High School What is a closed form solution?
  • · Replies 1 ·
Replies
1
Views
1K
High School New solutions to old, historic problems
  • · Replies 2 ·
Replies
2
Views
2K
High School What went wrong with (-x)^2=x^2?
  • · Replies 22 ·
Replies
22
Views
2K
High School Need an on-line calculator for a simple calculation
  • · Replies 12 ·
Replies
12
Views
4K
High School Sine Multiplication
  • · Replies 5 ·
Replies
5
Views
2K
High School Can a log have multiple bases?
  • · Replies 44 ·
2
Replies
44
Views
5K
High School Given an equation, find the value of this expression
  • · Replies 17 ·
Replies
17
Views
2K
High School Solving Simultaneous equations with cos() and sin()
  • · Replies 4 ·
Replies
4
Views
1K
High School English Translation of Italian Lecture Notes: Equations & Solutions
  • · Replies 11 ·
Replies
11
Views
2K
High School Tips on developing and improving number sense and basic math skills
  • · Replies 13 ·
Replies
13
Views
3K