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# Find the Maximum Number (Solution)

**00:00**
Infinity is a special value in the floating-point data type, which is greater than any other number. You can explicitly define infinity in Python by calling the built-in `float()`

function with a special string value as an argument, which says `"inf"`

.

**00:15**
There’s also negative infinity, which you can obtain by placing a minus sign (`-`

) in front of the positive infinity or by using the `"-inf"`

argument.

**00:28**
Now, unlike integers, Python floats do have a limit or maximum value. If you try to create a floating-point number that exceeds that limit, then you’ll get infinity instead. Here, I’m using `2e500`

, which gives me infinity.

**00:45**
However, to find the smallest exponent that yields infinity, I can use the bisection algorithm by halving the exponent value at each step. So, since `500`

is too much, I can try `250`

, which is half of the initial exponent. In this case, we’re getting a floating-point number that is clearly not infinity.

**01:07**
Let’s try something in the middle between `250`

and `500`

. That would be `375`

. Okay, that’s too much. We can try a smaller exponent by finding the middle point between the last two exponent values, which would be `250`

plus `375`

divided by `2`

. We can’t use fractional exponents, so we’ll round it to the nearest whole number, which is `312`

.

**01:36**
This also gives us infinity, so we have to keep trying smaller exponents. The next one should be `281`

.

**01:47**
Okay, that’s too small. Let’s move the other direction then.

**01:57**
We are getting closer now since the smallest exponents that we’re looking for must be somewhere between `297`

and `312`

.

**02:08**
Oh, we’re getting really close now since we only have a few numbers left to try. Why don’t we check them by hand? `306`

, that’s still too small.

**02:17**
`307`

, also too small. `308`

? Bingo. So the smallest exponent that gives us infinity is `308`

. That’s the answer. However, there’s a better way to find it.

**02:33**
This alternative approach is slightly more advanced, so don’t worry if you don’t completely understand it. You can import this standard library module called `sys`

, which provides access to system-specific parameters.

**02:45**
The parameter that we are interested in is called `float_info`

, and it shows a number of low-level details about the floating-point data type in Python, including `max_10_exp`

, which is equal to `308`

that we found manually. Note that this number isn’t set in stone, as it depends on your operating system, hardware, architecture, Python release, and how the Python interpreter was compiled.

**03:10**
So there’s no single correct answer to this exercise, as it may vary.

**03:16**
Okay, that wraps up this section. Next up, you’ll switch gears and get your hands dirty with number formatting.

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