# INF, NAN, and Null

**Inf**, **NAN**, and **Null** are special values, which can be very useful. Analytica returns them under conditions when it can't return a number. You can also type them directly into an expression or Edit table.

**Inf** means infinity, and is the result of dividing a positive number by zero -- e.g.,

`1/0 → Inf`

or computing a number larger than 1.796E308 (the largest number that your computer can represent in 64 bits) -- e.g.

`1E307 * 100 → Inf`

**-Inf** means negative infinity, the result of dividing a negative number by zero (or a number less than -1.796E308) -- e.g.

`-1/0 → -Inf`

**NAN** means "Not A Number". It is the result of a calculation that is not a well-defined number nor infinity -- e.g.

`0/0 → NAN`

`Sqrt(-1) → NAN`

(If you enable Complex Numbers, `Sqrt(-1)`

returns the valid imaginary number, *1j*.)

**Null** means that there is no such value. For example, Subscript returns `Null`

if the indexing value doesn't match a value of the Index:

`Index Year := [2015, 2016, 2017]`

`Slice(Year, 4) → NULL`

`Variable X := Array(Year, [20, 23, 28])`

`X[Year = 2018] → NULL`

You can also specify a different default result for an index value that doesn't match the index:

`X[Year = 2018, defValue: 0] → 0`

### More on INF and NAN

Calculations using `INF`

and `NAN`

follow ANSI (Association of National Standards Institutes) recommendations, which follow the laws of mathematics as far as possible:

`1/Inf → 0`

`1/(-Inf) → 0`

`Inf + Inf → Inf`

`Inf - Inf → NAN`

Expressions taking `NAN`

as an operand or parameter give `NAN`

as their result unless the expression has a well-defined logical or numerical value for any value of `NAN`

:

`True OR NAN → True`

`NaN AND False → False`

`IF True THEN 5 ELSE NAN → 5`

### More on NULL

When `Null`

appears in scalar operations, it generally produces a warning and evaluates to `Null`

, for example:

`10 + NULL → NULL`

`NULL - 10 → NULL`

`1 AND NULL → NULL`

Sum, Min, Max, ArgMax, JoinText, Npv, and other Array-reducing functions ignore `Null. For example:`

`Variable A :=`

I ▶ 1 2 3 4 5 8 NULL 4 NULL 0

`Sum(A, I) → 12`

`Average(A, I) → 4`

`JoinText(A, I, ', ') → "8, 4, 0"`

Graphs also ignore (do not show) any point whose value is `Null`

.

Some Array-reducing functions, notably Sum, Min and Max also accept an optional parameter «IgnoreNaN» to ignore `NaN`

values (which otherwise propagate, i.e. return `NaN`

).

Regression also ignores any data points which have `Y = Null`

, which is useful for missing data.

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