Is x=0 the Only Solution If x Is Less Than Every Positive Real Number n?

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Homework Help Overview

The discussion revolves around the mathematical assertion that if a real number "x" is less than every positive real number "n" and greater than or equal to zero, then "x" must be zero. Participants are exploring the implications of this condition within the context of real numbers.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants are considering the implications of "x" being non-zero and questioning what that would mean for "n". There is a suggestion of using proof by contradiction to explore the validity of the assertion. Some participants express confusion about the relationship between "x" and "n" and how to mathematically articulate their reasoning.

Discussion Status

The discussion is ongoing, with participants actively engaging in exploring different interpretations of the problem. Some guidance has been offered regarding proof techniques, but there is no explicit consensus on the next steps or conclusions.

Contextual Notes

Participants are grappling with the definitions and implications of the conditions set forth in the problem, particularly regarding the nature of positive real numbers and the constraints on "x".

transgalactic
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i got a real number called "x"

prove that if it follows this rule n>x>=0

for every real and positive "n"

then "x" must have the value x=0

??
 
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What do you think? Consider if x is non-zero... what can you say then?
 
if x is non zero then "n" is non zero too

what is the next step

??
 
Office Shredder is suggesting a proof by contradiction. Your next step is to think about what you need to do to carry out this proof. This is simple enough that you shouldn't have to ask for guidance at each and every step.
 
but from this expression
n>x>=0

"x" must not be equaled to 0

i can't see the way to solve it

??
 
They´re telling me that a positive real number x is smaller than ANY positive real number n. So n "pushes" x to the 0.

how to say that in math
 

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