# I am confused

$$\frac{1}{0}$$=$$∞$$

My teacher says this is undefined, while my calculator says this is true. Is this true or false?

Note by Alex Wang
1 year, 11 months ago

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Any number divided by zero is undefined.

- 1 year, 11 months ago

You first need to know that infinity is not a number. It doesn't follow simple algebra. Infinity is largest term that we cannot approach. Infinity depends on one's point of view to define.

- 1 year, 11 months ago

Your calculator will simply say whatever the programmers of said calculator told it to say for division by 0. Mathematically speaking though, division by 0 is undefined.

- 1 year, 11 months ago

Then why does the limit of 1/x as x approaches 0 approach $$∞$$?

- 1 year, 11 months ago

The limit of 1/x does indeed approach ∞ as x approaches 0+. (0+ meaning the positive side of the x-axis). That being said, it also has another limit: -∞, as x approaches 0-. (0- meaning from the negative side of the x-axis). This means that there are two limits of the function 1/x, and on extension, 1/0. Both ∞, and -∞. Since there is no single limit, it is undefined.

- 1 year, 11 months ago