Less, Equal, More

Counting is a useful craft but addition and multiplication may speed it up, often considerably. In this applet, you may click on each of the three numbers. Clicking a little to the right of its central line will increase the number by one. Clicking a little to the left of the number decreases the number by 1. The mathematical symbol ">" stands for more than, "<" stands for less than. You start with the common fact 1 + 1 = 2 which simply says that 2 denotes the number of elements in a group that is counted as "one and one", or which consists of two smaller groups each having 1 element. If you add an element to either of the smaller groups (or numbers on the left), to preserve the equality, you must also add a 1 on the right. (To change numbers faster, you can drag the mouse on the left or right of their central line.)

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