# Single most important object in mathematics?

1. Jul 15, 2009

### tgt

For me it would have to be the set of complex numbers. What's yours?

2. Jul 15, 2009

### mathman

Mathematics starts with the integers, so I would consider them the most important.

3. Jul 15, 2009

### turbo

The concept of zero, hands-down.

4. Jul 15, 2009

### Dragonfall

The von Neumann hierarchy.

5. Jul 15, 2009

### tgt

Well, the complex numbers include both of them (and also the reals).

6. Jul 15, 2009

### Office_Shredder

Staff Emeritus
From the empty set you can construct everything.

7. Jul 15, 2009

### AUMathTutor

I second the empty set.

8. Jul 16, 2009

### maverick_starstrider

To be accurate math starts (in the standard construction) with the natural numbers and sets. From there you derive integers, then rationals, then reals, then complex, then quaternions, then octernian, etc.

9. Jul 16, 2009

### pbandjay

Oh I'm totally all about Graham's number!

10. Jul 16, 2009

### flatmaster

How many dollars I have.

11. Jul 16, 2009

### dx

The ideas of 'set' and 'function'.

12. Jul 16, 2009

### g_edgar

the proof, Euclid I 47

13. Jul 16, 2009

### lormanv

The field of algebraic numbers.

14. Jul 16, 2009

### Dragonfall

So what's the LEAST important object in mathematics?

15. Jul 16, 2009

### maverick_starstrider

*insert offensive generalization about hygiene, women, etc.*.. oh snap!

16. Jul 17, 2009

### user111_23

1 is by far the most important.

17. Jul 17, 2009

### chiro

To me its the idea that representation of any kind is abstracted to a mathematical quantity. This fact alone says a lot about the power of mathematics.

18. Jul 18, 2009

### ƒ(x)

most important: equals sign?

19. Jul 18, 2009

### VeeEight

I third the empty set.

20. Jul 18, 2009

### camilus

$$e^{ix}= \cos (x)+ i \sin (x)$$
$$e^{i\pi}+1 =0$$