True or false?

Algebra Level 1

True or false :

$\quad$ For any real number $x$ , the value of $\{x\}$ can never be 1.

Notation : $\{ \cdot \}$ denotes the fractional part function .

True False

1 solution

Ashish Menon
May 18, 2016

For any integral values of $x$ , $\{x\}$ is $0$ because $[x] = x$ . But for any non-integral values if $x$ , $0 < \{x\} < 1$ . It can never be $1$ because the difference between the given number and its box function can never be $1$ .

If 2 < x then I think x can be 2 because it approaches 2 from above. If 0.999... = 1 , then I think it can be applied to that.

Kano Boom - 1 year, 5 months ago

The lower end should have an $\le$

A Former Brilliant Member - 5 years ago

Umm where?

Ashish Menon - 5 years ago

Nope, he specified: non-integral values.

Note: $\{x\} = x - \lfloor x \rfloor$ . Therefore, it should be $\lfloor x \rfloor = x$ in the first sentence

Hung Woei Neoh - 5 years ago

Umm isnt $[x]$ and $\left \lfloor x \right \rfloor$ same?

Ashish Menon - 5 years ago

@Ashish Menon – They are the same?

Hung Woei Neoh - 5 years ago

@Hung Woei Neoh – Yes, box function and floor function are the same as far as i know

Ashish Menon - 5 years ago

Ah, I didn't notice that.

A Former Brilliant Member - 5 years ago

True or false?

1 solution

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