Even in base π, π is still considered an irrational number; using an irrational based doesn't change the fundamental identity of whole numbers or irrational numbers, it just changes the way we write them.
Kinda. Technicaly no since an irrational number is a number that cannot be defined as a ratio of 2 existing rational numbers. Any number that can be represented in any rational base can by definition be represented as a ratio of somthing/base^n. This ignore the case of an irrational base but its practically useless cos any rational and most other irrational numbers will be irrational.
What u think ur trying to say is that some numbers cannot be represented in one base but can in another for example 1/3 can be represented as a decimal in base 3 but cannot jn base 10 ie u get 0.333(3 repeating forever).
Tieing back to floating point which uses base 2 u end up with simmillar issues with base10 base2 conversions hence most of the errors with floating point errors (yes at very large and very small numbers u lose accuracy but in practice most errors arise from base convention).
For future people here. They'll disable the link after a few days. When taking things off discord you have to now download the image, they no longer want to host things.
Each section of the binary number represents a different component needed to construct the number 300. It uses clever math to be able to represent decimals. It's like asking you whether a number is positive or negative, then the position of the decimal point, then what the digits are.
Specifically…
The first 0 means the number is positive. The number formed by the next eight bits (the exponent) and the number from the remaining bits (the mantissa) multiply to get 300.
The exponent bits choose the value of N in the formula 2^N-127^ . For the mantissa, we start with the number 1, then each "1" bit starting from the left adds to it 0.5, then 0.25, and so on. Specifically, we have 2^8^×1.171875.
Don't be irrational
But floating-point notation also can't precisely represent irrational numbers...
What superior method do you propose?
Following Pythagoreanism and believing irrational numbers to be blasphemous. They're represented by being struck down by the gods.
Symbolical computation is cool
But some irrational numbers are only so in base 10
What? That's not true at all...
Base π: π=1
Writing the same number a different way does not make it rational. There are no two natural numbers p and q so that p/q = 1 base pi.
Even in base π, π is still considered an irrational number; using an irrational based doesn't change the fundamental identity of whole numbers or irrational numbers, it just changes the way we write them.
1 is always 1. It's 1 × b⁰ where b is the base. Anything raised to the zeroth power is 1.
10 is the base. 1 × b¹ + 0 × b⁰
π = 10
in base 10, 10 = 10.
That doesn't make it rational but simply makes it writable in 2 digits(10)
Also you should have 3.1415... "number of characters" in that base... The base becoming irrational will make the number irrational
Kinda. Technicaly no since an irrational number is a number that cannot be defined as a ratio of 2 existing rational numbers. Any number that can be represented in any rational base can by definition be represented as a ratio of somthing/base^n. This ignore the case of an irrational base but its practically useless cos any rational and most other irrational numbers will be irrational.
What u think ur trying to say is that some numbers cannot be represented in one base but can in another for example 1/3 can be represented as a decimal in base 3 but cannot jn base 10 ie u get 0.333(3 repeating forever).
Tieing back to floating point which uses base 2 u end up with simmillar issues with base10 base2 conversions hence most of the errors with floating point errors (yes at very large and very small numbers u lose accuracy but in practice most errors arise from base convention).
FYI OP, Discord breaks external image links after a pretty short period.
For future generations:
I mean it's fine for me, but if it's broken for others I'll just use this one then.
For future people here. They'll disable the link after a few days. When taking things off discord you have to now download the image, they no longer want to host things.
For those who are curious, that's the IEEE 754 representation of the number 300.
Sigh, and I wanted to reply with
It's over 01000110000011001010000000000000!
Man that’s a big factorial
That was a very good guess!
What? Why?
Each section of the binary number represents a different component needed to construct the number 300. It uses clever math to be able to represent decimals. It's like asking you whether a number is positive or negative, then the position of the decimal point, then what the digits are.
Specifically…
The first 0 means the number is positive. The number formed by the next eight bits (the exponent) and the number from the remaining bits (the mantissa) multiply to get 300.
The exponent bits choose the value of N in the formula 2^N-127^ . For the mantissa, we start with the number 1, then each "1" bit starting from the left adds to it 0.5, then 0.25, and so on. Specifically, we have 2^8^×1.171875.
Aaaaaaaaaghhhh bitwise arithmetic aaaaaahhhhffggffg it's all coming back YOU DON'T KNOW WHAT YOU'VE UNLEASHED KHGHHAAAA
But thank you for the explanation
Honestly, as far as fresh takes on memes go, I loved that one quite a bit
Have had too many debates with senior programmers who don't understand why multiplying by 0.1 doesn't work.
"It works in , why doesn't it work in ?"
BigDecimal go brrrr
Where's my Lil'Endian ?
Such binary thinking.
I'm doing my part
someone xor this mfr rn fr