>>14340971Acting like a pretentious high schooler aside, you are on the verge of realising something important in mathematics. But you will only understand it if you learn to be skeptical of what you think now and refactor your understanding of mathematics.
"Easily described" is a layman's description of Kolmogorov complexity. You are implicitly assuming two things
1) That the numeric base system is the only means to encode numbers
2) That numbers must exist in some physical form to be "described"
To understand the answer to your question you first need to realise that the numeric base system is an algorithm, ie it is just a kind of computer program. The algorithm, which you were taught in middle school, is that its value is equal to its first position multiplied by 10^0, its second by 10^1, its third by 10^2 and so on.
Two answer the second assumption, like
>>14340979 will point out, many numbers do not have an accurate physical representation. When humans started doing mathematics, they used it to count. This is why it took so long to invent 0. Because they had to get over that habit of seeing numbers as things that necessarily physically exist. You can't show me a physical example of 0, by definition. You can however describe 0 to me, even if it doesn't physically exist.
Back to your OP. Can an integer be indescribable? In a purely numeric base system that must exist physically in some form, yes. But given any other system? It almost definitely can. Numeric systems are just a very narrow kind of descriptive system. The intuition behind Kolmogorov complexity is essentially how far can you compress an abstract idea.
