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What is ∞? I know it means infinity, but consider this:

[tex]\lim_{x\rightarrow +\infty} \frac{x^2 + 2x + 1}{x+1}[/tex]

Numerator: ##\displaystyle \lim_{x\rightarrow \infty} x^2 + 2x + 1## $$= \infty$$

Denominator: ##\displaystyle \lim_{x\rightarrow \infty} x + 1## $$= \infty$$

The numerator's ∞ is "bigger" than the denominator's, and the fraction tends to ##\frac{∞}{∞}## but I do NOT think it is equal to ##1##. Since it is ##\frac{big \infty}{small \infty}##, then it would ##= ∞##.

And more...

[tex]\lim_{x\rightarrow +\infty} \frac{x^2 + 2x + 1}{x+1} = \lim_{x\rightarrow +\infty} x+1 = ∞[/tex]

This is the same as ##\frac{big \infty}{small \infty} = \infty##. Doesn't this prove that the numerator's ##∞## is bigger than the denominator's?

[tex]\lim_{x\rightarrow +\infty} \frac{x^2 + 2x + 1}{x+1} = \lim_{x\rightarrow +\infty} \frac{x^2 + 2x + 1}{x+1}[/tex]

$$\frac{big \infty}{small \infty} = \lim_{x\rightarrow +\infty}\frac{(x + 1)^2}{(x + 1)}$$

$$\infty = \lim_{x\rightarrow +\infty} x + 1$$

$$\infty = \infty$$

Also, what is $$\frac{3\infty}{2\infty} ?$$

[tex]\lim_{x\rightarrow +\infty} \frac{x^2 + 2x + 1}{x+1}[/tex]

Numerator: ##\displaystyle \lim_{x\rightarrow \infty} x^2 + 2x + 1## $$= \infty$$

Denominator: ##\displaystyle \lim_{x\rightarrow \infty} x + 1## $$= \infty$$

The numerator's ∞ is "bigger" than the denominator's, and the fraction tends to ##\frac{∞}{∞}## but I do NOT think it is equal to ##1##. Since it is ##\frac{big \infty}{small \infty}##, then it would ##= ∞##.

And more...

[tex]\lim_{x\rightarrow +\infty} \frac{x^2 + 2x + 1}{x+1} = \lim_{x\rightarrow +\infty} x+1 = ∞[/tex]

This is the same as ##\frac{big \infty}{small \infty} = \infty##. Doesn't this prove that the numerator's ##∞## is bigger than the denominator's?

[tex]\lim_{x\rightarrow +\infty} \frac{x^2 + 2x + 1}{x+1} = \lim_{x\rightarrow +\infty} \frac{x^2 + 2x + 1}{x+1}[/tex]

$$\frac{big \infty}{small \infty} = \lim_{x\rightarrow +\infty}\frac{(x + 1)^2}{(x + 1)}$$

$$\infty = \lim_{x\rightarrow +\infty} x + 1$$

$$\infty = \infty$$

Also, what is $$\frac{3\infty}{2\infty} ?$$

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