Yes it is. Botanical name: Schlumbergera x buckleyi

Yes. What color is it supposed to be? farmerann

Yes it is and I would say that you got a bargain:o) If it is red maybe we can do some trading. If that is allowed on this forum. Mine is bright pink. Mine is at least 15 years old. It is blooming now. Late winter/early spring is the best time to take cuttings.
Best culture for this plant is bright indirect light. Can take some AM direct sun in winter. They love to go outside in summer in a shady, protected location. Soil should be well drained. Water well then let get nearly bone dry before watering again. Use half strength all purpose houseplant fertilizer (May-Sept), none in winter. I like to leave mine outside long enough to get some cool treatment (not freezing) in the fall to help with bud set. Hope this is helpful.

Dea

Looks like a easter cactus besides Christmas cactus this pic is of my Christmas cactus

see how pointy it is compares to urs urs is more rounded leaves then pointed mine is red in colour I paid $2.00 for mine whole pic mind is in about a 5" pot

Beautiful plants.

Matthew, yours is a Thanksgiving cactus.

Grantgarden2, yours is a true Christmas cactus.

Let's take a look at the two to remember how to ID these. The Thanksgiving cactus has saw-toothed projections on its stem segments or phylloclades. The Christmas cactus has rounded projections on its stem segments. The Easter cactus has fully rounded stem segments, with no projections.

All the best,

Maria Elena