×

# 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, 6 months ago

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$...$$ or $...$ to ensure proper formatting.
2 \times 3 $$2 \times 3$$
2^{34} $$2^{34}$$
a_{i-1} $$a_{i-1}$$
\frac{2}{3} $$\frac{2}{3}$$
\sqrt{2} $$\sqrt{2}$$
\sum_{i=1}^3 $$\sum_{i=1}^3$$
\sin \theta $$\sin \theta$$
\boxed{123} $$\boxed{123}$$

Sort by:

Any number divided by zero is undefined.

- 1 year, 6 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, 5 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, 6 months ago

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

- 1 year, 6 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, 6 months ago