If: 1^x=1^y and as: 1^2=1^99 then: 1=99

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

Discussion Overview

The discussion revolves around the mathematical assertion that if \(1^x = 1^y\) and \(1^2 = 1^{99}\), then it follows that \(1 = 99\). Participants explore the validity of this claim, examining the implications and underlying reasoning.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant asserts that \(1^x = 1^y\) leads to the conclusion \(1 = 99\), based on the example \(1^2 = 1^{99}\).
  • Another participant questions the validity of the assertion, suggesting that the reasoning is flawed and comparing it to the equation \(1 \cdot 0 = 99 \cdot 0\).
  • A third participant points out that taking the logarithm of the equation would yield different results, indicating a misunderstanding in the application of the function.
  • One participant introduces the concept of functions and their properties, arguing that certain functions cannot satisfy the condition \(f(x) = f(y) \Leftrightarrow x = y\) in this context.
  • Another participant humorously parallels the discussion with a flawed logic example involving trigonometric functions, suggesting that the reasoning is absurd.
  • A participant reiterates the original assertion, breaking down the left-hand side and right-hand side of the equation to demonstrate equality, but does not clarify the transition between steps.
  • One participant expresses enjoyment of the discussion, indicating a light-hearted tone amidst the debate.

Areas of Agreement / Disagreement

Participants do not reach a consensus; multiple competing views remain regarding the validity of the original assertion and the reasoning behind it.

Contextual Notes

There are limitations in the assumptions made about the properties of exponentiation and functions, as well as the implications of using zero in multiplication, which remain unresolved.

nabodit
Messages
16
Reaction score
0
if:
1^x=1^y
and as:
1^2=1^99
then:
1=99
 
Mathematics news on Phys.org
Why do think this is true?

Since 1*0=99*0, do you consider this as proof of your assertion as well?
 
Last edited:
The log of your equation would beg to differ... EDIT: except you consistently used 1, not a variable. Duh! Mondays are rubbish. Anyway, shouldn't that read 2 = 99?
 
Last edited:
I don't know if it's a joke or not.
If you have a function f(x) such that [itex]f(x_0) \neq f(x_1)[/itex], for all [itex]x_0 \neq x_1[/itex]. Just in that case, you will have [itex]f(x) = f(y) \Leftrightarrow x = y[/itex]
Some function like :f(x) = 0x, f(x) = 1 ^ x, f(x) = x ^ 0 ([itex]x \in \mathbb{R} - \{ 0 \}[/itex]). You cannot have [itex]f(x) = f(y) \Leftrightarrow x = y[/itex]. Why? Because in that 3 examples:
[itex]\forall x, f(x) = const[/itex]
Viet Dao,
 
Last edited:
sin(0) = sin(2 pi)

Oh no! 2 pi = 0, meaning pi = 0, which means circles don't exist!

If only there was a flaw in the logic...
 
nabodit said:
1^2=1^99
then:
1=99
LHS = 1*1 = 1
RHS = 1*1*1* ...(ninety five times) *1 = 1
LHS = 1 = RHS

How do you go from line (1) to line (2) ?

nabodit : If you have a question to ask, ask it now.
 
Reading this really brightened up my day. :smile:
 

Similar threads

High School Potato paradox
  • · Replies 28 ·
Replies
28
Views
4K
High School 1lb cube of 99% pure copper?
  • · Replies 10 ·
Replies
10
Views
4K
MHB Smallest Number Divisible by 99 Using Digits 1-9
  • · Replies 1 ·
Replies
1
Views
2K
MHB Prove Product of Polynomials: No Odd Degree Terms
  • · Replies 1 ·
Replies
1
Views
1K
MHB Is the Inequality of Series Proven with 1 to 99 and 2 to 100?
  • · Replies 2 ·
Replies
2
Views
2K
MHB Prove Inequality: $18<\sum\limits_{i=2}^{99}\dfrac 1{\sqrt i} <19$
  • · Replies 2 ·
Replies
2
Views
1K
Why Does Expanding (13-8)^99 Not Yield the Same Remainder as 5^99 Modulo 13?
  • · Replies 7 ·
Replies
7
Views
2K
High School Googol and number naming scheme (Was: Just for fun)
  • · Replies 10 ·
Replies
10
Views
2K
MHB Solving Trig Identity: Sin[1/2 sin^−1 (x)] = 1/2 X (sqr(1+x) –sqr(1-x))
  • · Replies 2 ·
Replies
2
Views
2K
High School Can you solve the equation 100! - 99!?
  • · Replies 5 ·
Replies
5
Views
3K