A problem with a septimal system.

[usermath]

I'm reading a textbook of mathematics 'What is mathematics?' and I've got a problem with septimal system.

Symbol 10416 in the septimal system denote 2610 (decimal system).

$1*7^4+0*7^3+4*7^2+1*7+6 = 2610$

But I can't understand why 7416 in the septimal system denote 2610 too.

$7*7^3+4*7^2+1*7+6 = 2610$

Where is my mistake?

 

[Orodruin]

In base N you only use numbers 0 to N-1.

Examples:
Binary (base 2): 0 and 1
Decimal (base 10): 0 to 9
etc

 

[ehild]

The digit "7" does not exist in the septimal system.

ehild

 

[usermath]

Ok. I see. In the septimal system a base is 7 i.e. 0 to 6. I thought 1 to 7. It was my mistake.

Thanks for your answers.

 

[SteamKing]

Also, 7*7^3 = 7^4, whatever system you are using.

 

[usermath]

7*7^3 = 7^4

Thank you.