If a/x*x = a then if x =0 a/0*0 = a

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

Discussion Overview

The discussion revolves around the implications and interpretations of division by zero, particularly in the context of mathematical definitions and the behavior of functions as they approach zero. Participants explore various perspectives on whether expressions involving division by zero can be defined or understood in a meaningful way, touching on concepts such as infinity and undefined values.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants argue that if \( a/x \cdot x = a \), then substituting \( x = 0 \) leads to contradictions, as \( a/0 \cdot 0 \) should equal \( a \) but is also claimed to equal 0.
  • Others assert that division by zero is undefined, emphasizing that \( a/0 \) does not equal 0 and that anything divided by zero is not defined in standard mathematics.
  • A historical perspective is introduced, noting that certain mathematical concepts were once considered impossible until new definitions, like imaginary numbers, were developed.
  • Some participants discuss the implications of defining a number system where division by zero is allowed, suggesting it would lead to every number being equal, which they find uninteresting.
  • There is confusion among participants regarding whether \( 1/0 \) should be considered undefined or infinite, with some suggesting that if \( 1/0 \) were infinite, it would lead to contradictions.
  • Discussions about limits arise, with some participants noting that as \( x \) approaches 0 in the function \( y = 1/x \), \( y \) approaches infinity, while others argue that this is still considered undefined.
  • Participants explore the concept of indeterminate forms, particularly \( 0 \cdot \infty \), and how these forms are treated in calculus.
  • Some participants express that while division by zero is undefined in real numbers, it may have different interpretations in applied contexts or limits.
  • There is a discussion about the existence of zero and infinity in reality, with differing opinions on whether these concepts can be physically realized.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the definitions and implications of division by zero. There are multiple competing views regarding whether expressions involving zero and infinity can be defined, and the discussion remains unresolved.

Contextual Notes

Limitations include the dependence on definitions of mathematical terms, the ambiguity surrounding the treatment of infinity, and the unresolved nature of certain mathematical expressions involving division by zero.

  • #31
Hey Alkatran, you ever going to concede the point in eot-cat-cit?
 
Mathematics news on Phys.org
  • #32
Alkatran said:
How do you know time is caused by motion? That makes very little sense. It makes more sense to say motion is caused by the passage of time.

yes, sort of. Actually it is impossible for creaters which are under time and motion, to knwo which one is more fundamental. But if nothing moves then there is no time.
 
  • #33
if time is relative to the observer, then it is possible for time not to "flow" at all. like if u observe a foton, it does not have any "flowing" time at all
 
  • #34
ArielGenesis said:
if time is relative to the observer, then it is possible for time not to "flow" at all. like if u observe a foton, it does not have any "flowing" time at all

yes: time is relative. photons, for example, have infinite life, although can be created and destroyed.
 
  • #35
This thread has completely digressed from the OP's question, which itself is not a brain teaser, but a question asking for clarification of the definition of the reals.
 

Similar threads

Undergrad Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
  • · Replies 16 ·
Replies
16
Views
1K
High School About a definition: What is the number of terms of a polynomial P(x)?
  • · Replies 48 ·
2
Replies
48
Views
4K
Undergrad Why is 1 not equal to 0 in this proof?
  • · Replies 66 ·
3
Replies
66
Views
7K
Graduate A global version of the implicit function theorem
  • · Replies 0 ·
Replies
0
Views
642
High School Popularizing a property for n-bonacci numbers without publishing it?
  • · Replies 12 ·
Replies
12
Views
2K
High School Why are the values (-1.618, 0) and (0.618 ,0) solutions for this equation?
  • · Replies 44 ·
2
Replies
44
Views
5K
MHB Solve Equation: $x^4+2x^3-x^2-6x-3=0$
  • · Replies 7 ·
Replies
7
Views
2K
High School Nonsense can be truth in logic?
  • · Replies 84 ·
3
Replies
84
Views
7K
MHB Equation 2: Prove that ##x^2+2x\sqrt x+3x+2\sqrt x+1=0##
  • · Replies 4 ·
Replies
4
Views
2K
MHB Interpolating Points with Continuous Modular Functions?
  • · Replies 5 ·
Replies
5
Views
2K