Greatest integer functions, anyone?

Number Theory Level 3

Evaluate $\lfloor{2.99999999......}\rfloor$ . Here, $\lfloor {x} \rfloor$ denotes the greatest integer not exceeding $x$ , for all reals $x$ .

2 Not defined 3 1

1 solution

Shourya Pandey
Apr 22, 2016

$2.99999...$ is exactly $3$ , so the answer is $3$ .

Infinitesimally it's less than 3, so how can it be 3?

Siva Bathula - 5 years, 1 month ago

"Infinitesimal" is not a number.

Shourya Pandey - 5 years, 1 month ago

Yes, its a real number which is less than 3, but the limit value is 3?

Siva Bathula - 5 years, 1 month ago

@Siva Bathula – $2.99999...$ is itself DEFINED as a limit.

Shourya Pandey - 5 years, 1 month ago

@Shourya Pandey – Shourya do this way .. Write that as 2 + 0.9999..... And now prove that 0.999999.. =1 . Btw how are you doing ? What rank do u expect this jee mains ?

Pawan pal - 5 years, 1 month ago

Greatest integer functions, anyone?

1 solution

0 pending reports