In mathematics, in order not to write or draw many things, we normally use symbols, which summarize an idea.
For example, this is the equal symbol. So when two things are the same, we put the symbol between them.
So if I have a box, and I say that it equals another box, and inside the box is an apple, then that will only be the same if when I take the other box out, I find an apple inside.
Thus, an apple is like an apple. Remember that math is the art of understanding. And understanding has several details. An apple can only be really the same if it is the same apple. But in mathematics we may be concerned with quantity, so apples may not be the same, but they are considered equal. Normally, when we use the same in mathematics, we are concerned with quantity, not with the object itself.
But there may be cases in which we are concerned with the characteristic, and then the two objects must be equal, not only in quantity, but in essence.
The other symbol is different, and different is the opposite of the same. So everything that is different is not the same.
Another symbol is the Biggest, so a big apple is bigger than a small apple, and the bigger symbol is between the two, and we say that the apple on the left is bigger than the apple on the right.
The other symbol is the Minor, so a small apple is smaller than a large apple, and so we say that the apple on the left is smaller than the apple on the right.
We can still have the Greater or equal symbol, and also the Less or equal symbol.
Thus, two equal apples can be Greater or equal, or Less and equal. But couldn't we use the same symbol then?
Yes we could, but imagine that we want all apples that are bigger and the same as the one I have. So, I would use the Greater or equal to get all apples that were larger or equal.
The same thing would be with the smaller and the same.
Another symbol is belonging, which determines that an object belongs to a specific group. Thus, a blue house belongs to the group of blue things.
Or the ball belongs to the toy group.
Or the cell phone belongs to the group of electronic devices.
We also have what does not belong, when the object is not part of the group.
So, the ball we are seeing does not belong to the group of blue things.
And the house does not belong to the group of electronic devices.
But the cell phone may belong to the toy group. It depends on whether you consider the cell phone a toy or not.
But in mathematics that is based on truth, then things are defined correctly, so that something is true or false.
