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{$x$} is like the fractional part: x - floor(x)

$[x]$ is the whole part or whatever it's called: floor(x)

AnalysisStudent0414
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questionasker22
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  • Why would you say that ? – TheSilverDoe Nov 26 '20 at 12:37
  • it's the first number that comes to mind and {x} is between [0,1) and if you were to take a rational number per say 0.75 [x] would be 0 and {x} would be 0.75 and they don't coincide :DD hope my way of thinking makes sense but it's certainly wrong – questionasker22 Nov 26 '20 at 12:38
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    No it is correct :) $\lbrace x \rbrace$ must be in $[0,1)$, and $[x]$ must be an integer, so.......... – TheSilverDoe Nov 26 '20 at 12:39
  • I don't understand what's the question here. –  Nov 26 '20 at 14:10
  • @Nikhil The question has been savagely edited, si it is now unreadable : it asked to find all the numbers $x$ such that $\lbrace x \rbrace = [x]$. – TheSilverDoe Nov 26 '20 at 18:51

2 Answers2

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$$x - [x] = [x]$$ $$x = 2[x]$$

Since $[x]$ is an integer, then $x$ is also an integer. But then $x=[x]$, so you have $$x = 2x$$

to which $x=0$ is the only solution.

AnalysisStudent0414
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1

You're right.

$[x]$ is an integer and $\{x\}$ is in the interval $[0,1)$. The only integer in that interval is $0$.

Thus, $\{x\} = [x]$ implies $\{x\}=0$ and so $x=0$.

lhf
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