I have started reading a book called 'What is Mathematics?' by Ian Stewart, and there he explains the number system with a base of 7. Septimal number system. I don't understand how one may write 7^2 in such a system, since we only have numbers 0-6. I don't understand how we represent numbers that exceed symbols we can use from. For eg: 4+4 is given to be '11' instead of '8'. How did we come up with '11'?
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How do you write eleven in the decimal system when you have only digits 0 to 9? – Magdiragdag Apr 10 '21 at 09:42
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You realize that in decimal numbers, $342=3 \cdot 10^2+4 \cdot 10^1 + 2 \cdot 10^0$, right? What do you think $342_7$ would mean? – Robert Shore Apr 10 '21 at 09:54
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$7^2=1\times7^2+0 \times 7^1+0\times7^0=100_7^{,}$ while $11_7^{,}=10_7^{,}+1_7^{,}=1\times 7^1+1\times7^0=8$ – Henry Apr 10 '21 at 10:06
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Thanks a lot people for the explanations. It is much clearer now. – SnappedOutside Apr 13 '21 at 11:13