yes.
You need a lot of things, unless you are raising goldfish in a bowl. You need: (for a tank) A filter A tank (not recommended under 5 gal.) Goldfish food Gravel Live or fake plants (underwater plants) Air pump (not required) Choice of decorations These can be very expensive sometimes, but it will keep your goldfish living longer and happier than in a bowl
A goldfish does not need an airpump, it needs 3 stage filtration and good water movement from something such as a box filter and/or power heads. A goldfish, however, is not suited for a 5 gallon tank. 10 gallons per goldfish is the recommended minimum, as they grow very large and require more oxygen than almost any other fish. I would recommend something smaller such as rosy minnows, guppies, or if you get a heater, small tropical fish like tetras. ALL fish however, need filtration, not just an air pump.
No, however a goldfish will greatly benefit from having one. An air pump provides an added source of aeration which increases the levels of dissolved oxygen in the tank. This in-turn makes it easier for the fish to breath.
While it isn't required that goldfish have an air pump in their tank. It can help your tank life by providing valuable oxygen to the fish. This isn't specific to just goldfish, as all aquatic life can benefit from the presence of a air pump. If you notice your fish swimming with their lips on top of the water level most likely they are trying to get air. This is especially true for tanks that have canister or over flow filters where the water is pumped and filtered without making contact with air.
They don't have to have one but it's better for them and they will live longer if you do.
Actually, I think that temperature is about right for your goldfish. But if you seriously need to, you need to change the temperature of the air around the tank. I suggest keeping it in a cooler room?
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They definitely need a air pump, a filter, at least 20 gallons of water for one goldfish, a thermometer, and decorations to improve the goldfish's well-being/mood.
That is completely normal.
You need an air pump and a filter in your tank to purify the water. Along with that the nitrogen cycle for the fish will not be disturbed as well as there being more oxygen for the fish to breath.
You will need to connect the air. Professor to the water pump. The air going into the well will force the water upward.