hahaha base 1 is so unpractical. You are right. But you can count in base 2 on your hands. Just look at your hand (I do it palm up) and clench your fist. This is 0.

Then whether your fingers are extended or in your fist represents the 0 or 1 in the base 2 system. For instance, if I look at my hand palm up, and raise only my thumb, that's 2^0 = 1. The next number is your index finger up only, because that's 10 = 2^1 + 0 = 2, and so on. It takes practice but using this improved hand-counting method, you can count from 0 to 2^5-1 (31) on only one hand.

Using two hands you can count up to 2^10 -1 = 1023 but using two hands is cumbersome and if you have to count that high, there are better ways than using your hand. But one hand is kinda cool. Warning, however, that representing the number 4 with this base-2 hand counting is the middle finger, and may cause offense to those not familiar with this counting system.

My francais est non existante, but did you say that base 1 doesn't exist??? Man, base 1 is the oldest base there is. Base 1 exists and is a well-defined base. Like all other positive integral bases, a number in base 1 can be thought of as a sum of powers of 1. For instance 1001 in base 2 is 2^3 + 2^0 = 9. That we can agree I'm sure.

Then there is base 1, which has a single numeral, which I shall represent by the symbol "1". It just means "one". 111 = 1^1 + 1^1 + 1^1 = 3, for instance. Base 1 is the familiar counting by making scratch marks on a club to count how many apes you killed for brunch. Making five tick marks: 11111 just means [5]_10, that is, five in base ten. To convert from base 1 to base 10, just add up all the tick marks, and to go back, write the number of tick marks. So 6 in base 1 is 111111. Obviously you get it, and I'm just going into detail. But we all know what base 1 is, because all of us use it.

I mean, base 1 is the most primitive form of counting.

And what's the next number after 1? In base one it's 11. Obviously - two tick marks comes after one tick mark, right? So 1 + 1 = 11. <----this is truth, in base 1.