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.

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.

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.

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`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

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Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

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`\boxed{123}`

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TopNewestAny number divided by zero is undefined.

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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.

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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.

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Then why does the limit of 1/x as x approaches 0 approach \(∞\)?

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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.

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