is-1-1-1-1-or-1-1-1-1-1-1-

Question Number 88610 by M±th+et£s last updated on 11/Apr/20

i s 1 \times 1 \times 1 \times \dots \dots \dots . = 1^{\infty}

o r

1 \times 1 \times 1 \times 1 \times 1 \times \dots \dots \dots . = 1

Commented by mahdi last updated on 11/Apr/20

for example :

A) \lim_{x \to \infty} {(1 + \frac{1}{x})}^{x} = 1^{\infty} = e \neq 1

B) \lim_{x \to \infty} (1^{x}) = 1^{\infty} = 1 = 1

in A : 1 \times 1 \times \dots = 1^{\infty} \neq 1 B : 1 \times 1 \times \dots = 1^{\infty} = 1

Question is important .

Commented by M±th+et£s last updated on 11/Apr/20

a n d t h e r e i s m o r e e x a m p l e s l i k e

\underset{x \to \infty}{l i m} {(1 + \frac{1}{x^{2}})}^{x} = 1

\underset{x \to \infty}{l i m} (1 + \frac{1}{l o g (x)}) = \infty

\underset{x \to \infty}{l i m} {(1 - \frac{1}{l o g (x)})}^{x} = 0

s o i t h i n k t h a t i t s n o t w r o n g i f w e s a y t h a t 1 \times 1 \times 1 \times 1 \times \dots . . = 1^{\infty} = 1

b u t n o t i n e v e r y t i m e 1 \times 1 \times 1 \times 1 \dots . . = 1^{\infty}