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Well, as of 1990, 5 states of matter had been Proven to exsist.

1. Solid

2. Liquid

3. Gas

4. Plasma

5. Bose-Einstien Condensate

Now, if you want to include some more exotic, experimental, and theoretical states of matter, then the number of states of matter can reach up to 19-22. Keep in mind that some of these are only theoretical, and that some are proven. But some of these include:

1. Superliquids

2. Fermionic Condensate

3. Symmetrical Matter

And many more.

You may also want to include supercritical fluids (as distinct from superliquids). It is possible to go between a gas and a liquid without ever undergoing a phase change if you craft the path to go through the supercritical region. A substance is defined to be a supercritical fluid when it is above its critical temperature and pressure. Above the critical pressure, no change in temperature can cause the fluid to boil or condense. Above the critical temperature, no pressure change can cause a fluid to evaporate or liquefy. Sufficient increase in pressure or decrease in temperature can still get a substance to solidify even if it is supercritical. To understand why a supercritical state can occur, remember that as you increase the temperature of a liquid, it becomes less dense - it expands (that's why thermometers work). As you increase the pressure on a gas, it becomes more dense. As you continue to increase temperature and pressure, the densities of the gas and liquid that are in equilibrium at the "boiling point" get closer and closer until they become the same at the critical temperature and pressure. Above that point, no phase transition between liquid and gas is possible any more because they have merged into one phase.

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