Infinity symbol

The infinity symbol is a mathematical symbol that represents an infinitely large number.

The infinity symbol is written with the Lemniscate symbol:

It represents an infinitely positive big number.

When we want to write an infinitely negative number we should write:

-∞

When we want to write an infinitely small number we should write:

1/∞

Is infinity a real number?

Infinity is not a number. It does not represent a specific number, but an infinitely large quantity.

Infinity rules & properties

Name Key type
Positive infinity
Negative infinity -∞
Infinity difference ∞ - ∞ is undefined
Zero product 0 ⋅ ∞ is undefined
Infinity quotient ∞ / ∞ is undefined
Real number sum x + ∞ = ∞, for x∈ℝ
Positive number product x ⋅ ∞ = ∞, for x>0

How to type infinity symbol on keyboard

Platform Key type Description
PC windows Alt+236 Hold the ALT key and type 236 on the num-lock keypad.
Macintosh Option+5 Hold the Option key and press 5
Microsoft word Insert > Symbol > ∞ Menu selection: Insert > Symbol > ∞
Alt+236 Hold the ALT key and type 236 on the num-lock keypad.
Microsoft excel Insert > Symbol > ∞ Menu selection: Insert > Symbol > ∞
Alt+236 Hold the ALT key and type 236 on the num-lock keypad.
Web page Ctrl+C, Ctrl+V Copy ∞ from here and paste it in your web page.
HTML &infin; or &#8734;
ASCII code 236
Unicode U+221E
LaTeX \infty
MATLAB \infty Example: title('Graph to \infty')

Infinity in set theory

Aleph-null () is the infinite number of elements (cardinality) of the natural numbers set ().

Aleph-one () is the infinite number of elements (cardinality) of the countable ordinal numbers set (ω1).

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